Edit Profile (opens in new tab) Martynyuk, Anatoliĭ Andriĭovych Compute Distance To: Compute Author ID: martynyuk.anatoly-a Published as: Martynyuk, A. A.; Martynyuk, Anatoly A.; Martynyuk, Anatoliy A.; Martynyuk, Anatoliy; Martynyuk, Anatolii A.; Martynyuk, Anatoliĭ A.; Martynyuk, Anatoly; Martynyuk, À. À.; Martynyuk A. A.; Martynyuk, A. Further Spellings: Мартынюк Анатолий Андреевич Homepage: http://www.martynyuk.kiev.ua/ External Links: Wikidata · Math-Net.Ru · dblp · IdRef Documents Indexed: 472 Publications since 1967, including 28 Books 4 Contributions as Editor · 1 Further Contribution Reviewing Activity: 1,065 Reviews Biographic References: 3 Publications Co-Authors: 137 Co-Authors with 279 Joint Publications 3,690 Co-Co-Authors all top 5 Co-Authors 196 single-authored 28 Nikitina, Nelly Vladimirovna 18 Martynyuk-Chernienko, Yu. A. 18 Slyn’ko, Vitalii Ivanovich 15 Chernetskaya, Larisa Nikolaevna 13 Mytropol’skyĭ, Yuriĭ Oleksiĭovych 12 Luk’yanova, T. A. 12 Miladzhanov, V. G. 12 Stamova, Ivanka Milkova 11 Khoroshun, A. S. 10 Lila, D. M. 8 Lakshmikantham, Vangipuram 8 Stavroulakis, Ioannis P. 7 Aleksandrov, Aleksandr Yur’evich 7 Kozubovskaya, I. G. 7 Samoĭlenko, Anatoliĭ Mykhaĭlovych 6 Il’in, Vladimir Aleksandrovich 6 Leela, Srinivasa G. 6 Obolenskii, A. Yu. 6 Stamov, Gani Trendafilov 6 Yanishevskiĭ, A. P. 5 Begmuratov, K. A. 5 Chernienko, V. A. 5 Gaĭshun, Ivan Vasil’vich 5 Mishchenko, Evgeniĭ Frolovich 5 Rozov, Nikolaĭ Khristovich 5 Sun, Zhenqi 4 Dshalalow, Jewgeni H. 4 Freedman, Herbert Irving 4 Izobov, Nikolaĭ Alekseevich 4 Karimzhanov, A. 4 Kiguradze, Ivan Tarielovich 4 Kirichenko, N. F. 4 Kudryavtsev, Lev Dmitrievich 4 Pliss, Viktor Aleksandrovich 4 Shemyakina, Tamara Kuz’minichna 3 Babenko, Sergei V. 3 Chernienko, A. N. 3 Platonov, Alekseĭ Viktorovich 3 Sukennik, A. A. 3 Zadorozhny, Vladimir F. 2 Anosov, Dmitriĭ Viktorovich 2 Babenko, Ekaterina A. 2 Bohner, Martin J. 2 Boĭchuk, Oleksandr Andriĭovych 2 Borisenko, S. D. 2 Denisenko, V. S. 2 Gojsa, L. N. 2 Grujić, Ljubomir T. 2 Ivanov, I. L. 2 Khusainov, Denis Ya. 2 Kondrat’ev, Vladimir Aleksandrovich 2 Korovin, Sergeĭ Konstantinovich 2 Kosolapov, V. I. 2 Kozhukhovskii, N. N. 2 Kozlov, Valeriĭ Vasil’evich 2 Krapivnyj, Yu. N. 2 Kurzhanskiĭ, Aleksandr Borisovich 2 Matvijchuk, K. S. 2 Mazko, Alexey G. 2 Millionshchikov, Vladimir Mikhaĭlovich 2 Rasshyvalova, S. N. 2 Ribbens-Pavella, Mania 2 Rizaev, A. 2 Sergeev, Igor’ Nikolaevich 2 Sivasundaram, Seenith 2 Vladimirov, Vasiliĭ Sergeevich 2 Zhukovskiĭ, Vladislav Iosifovich 1 Abrashin, Vyacheslav Nikolaevich 1 Arutyunov, Aram Vladimirovic 1 Bibikov, Yuriĭ Nikolaevich 1 Bogdanova, S. S. 1 Bulgakov, Aleksandr Ivanovich 1 Burton, Theodore Allen 1 Chernienko, V. O. 1 Cruz-Hernández, César 1 Defoort, Michael 1 Djemai, Mohamed 1 Dzhalalov, E. E. 1 Emel’yanov, Stanislav Vasil’evich 1 Graef, John R. 1 Grygorenko, Yaroslav Mykhaĭlovych 1 Hamaya, Yoshihiro 1 Kato, Junji 1 Kats, I. Ya. 1 Korolyuk, Volodymyr Semenovych 1 Koshlyakov, Vladimir Nikolaevich 1 Kovalev, Alexander M. 1 Krapivnyi, Yu. N. 1 Kravchenko, Viktor Filippovich 1 Larin, Vladimir Borisovich 1 Lila, S. 1 Lukovsky, Ivan Oleksandrovych 1 Lula, D. M. 1 Makarov, Evgeniĭ Konstantinovich 1 Maksimov, Vladimir Petrovich 1 Martynyuk, Vladislav A. 1 Mazanik, Sergeĭ Alekseevich 1 Moiseev, Evgeniĭ Ivanovich 1 Mullazhonov, R. V. 1 Muminov, M. M. ...and 37 more Co-Authors all top 5 Serials 49 Prikladnaya Mekhanika 41 Soviet Applied Mechanics 40 Dopovidi Natsional’noï Akademiï Nauk Ukraïny. Matematyka, Pryrodoznavstvo, Tekhnichni Nauky 34 Nonlinear Dynamics and Systems Theory 30 International Applied Mechanics 27 Ukraïns’kyĭ Matematychnyĭ Zhurnal 17 Ukrainian Mathematical Journal 15 Dopovidi Akademiï Nauk Ukraïns’koï RSR. Seriya A 14 Differential Equations 13 Soviet Mathematics. Doklady 13 Doklady Mathematics 8 Differential Equations 7 Russian Academy of Sciences. Doklady. Mathematics 7 Zagadnienia Drgań Nieliniowych 6 Differentsial’nye Uravneniya 6 Journal of Mathematical Sciences (New York) 6 Matematicheskaya Fizika 5 Teorijska i Primenjena Mehanika 5 Stability and Control: Theory, Methods, and Applications 5 Nonlinear Analysis. Theory, Methods & Applications 4 Differential Equations and Dynamical Systems 4 Nonlinear Oscillations 3 Journal of Mathematical Analysis and Applications 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 Journal of Applied Mathematics and Stochastic Analysis 3 Communications in Applied Analysis 3 Pure and Applied Mathematics, Marcel Dekker 3 Nonlinear Analysis. Hybrid Systems 3 Stability, Oscillations and Optimization of Systems 2 Applicable Analysis 2 Doklady Akademii Nauk Ukrainskoĭ SSR, Seriya A 2 International Journal of Non-Linear Mechanics 2 Rocky Mountain Journal of Mathematics 2 Chaos, Solitons and Fractals 2 Avtomatika 2 Dopovidi Akademiï Nauk Ukraïni 2 The Canadian Applied Mathematics Quarterly 2 Matematychni Metody ta Fizyko-Mekhanichni Polya 2 Systems & Control: Foundations & Applications 2 Pure and Applied Mathematics (Boca Raton) 1 Soviet Journal of Nuclear Physics 1 Stochastic Analysis and Applications 1 Soviet Journal of Automation and Information Sciences 1 Differential and Integral Equations 1 Panamerican Mathematical Journal 1 Automation and Remote Control 1 Neural, Parallel & Scientific Computations 1 Journal of Automation and Information Sciences 1 Electronic Journal of Differential Equations (EJDE) 1 Visnyk. Seriya: Fizyko-Matematychni Nauky. Kyïvs’kyĭ Universytet Imeni Tarasa Shevchenka 1 Communications in Nonlinear Science and Numerical Simulation 1 Trudy Instituta Matematiki 1 Nonlinear Analysis. Real World Applications 1 Nonlinear Analysis. Modelling and Control 1 Dynamics of Continuous, Discrete & Impulsive Systems. Series A. Mathematical Analysis 1 Cubo 1 Lecture Notes in Control and Information Sciences 1 Libertas Mathematica. New Series 1 International Journal of Systems Science. Principles and Applications of Systems and Integration all top 5 Fields 326 Ordinary differential equations (34-XX) 136 Systems theory; control (93-XX) 117 Mechanics of particles and systems (70-XX) 42 Dynamical systems and ergodic theory (37-XX) 28 History and biography (01-XX) 20 Difference and functional equations (39-XX) 12 Mechanics of deformable solids (74-XX) 12 Biology and other natural sciences (92-XX) 8 Real functions (26-XX) 8 Partial differential equations (35-XX) 7 Integral equations (45-XX) 6 Probability theory and stochastic processes (60-XX) 6 Numerical analysis (65-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 General and overarching topics; collections (00-XX) 3 Measure and integration (28-XX) 3 Operator theory (47-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Computer science (68-XX) 2 Optics, electromagnetic theory (78-XX) 1 Mathematical logic and foundations (03-XX) 1 Combinatorics (05-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Functional analysis (46-XX) 1 General topology (54-XX) 1 Fluid mechanics (76-XX) 1 Quantum theory (81-XX) 1 Geophysics (86-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 192 Publications have been cited 1,023 times in 648 Documents Cited by ▼ Year ▼ Stability analysis of nonlinear systems. Zbl 0676.34003Lakshmikantham, V.; Leela, S.; Martynyuk, A. A. 255 1989 Practical stability of nonlinear systems. Zbl 0753.34037Lakshmikantham, V.; Leela, S.; Martynyuk, A. A. 91 1990 Practical stability of motion. (Практическая устойчивость движения.) Zbl 0539.70031Martynyuk, A. A. 23 1983 Stability by Lyapunov’s matrix function method with applications. Zbl 0907.34034Martynyuk, A. A. 21 1998 Stability of motion: the comparison method. Stability: theory, methods and applications. (Устойчивость движения: метод сравнения. Устойчивость: теория, методы и приложения.) Zbl 0852.34057Lakshmikantham, V.; Leela, S.; Martynyuk, A. A. 21 1991 Large scale systems stability under structural and singular perturbations. Zbl 0649.93003Grujić, Lj. T.; Martynyuk, A. A.; Ribbens-Pavella, M. 19 1987 The Lyapunov matrix-function. Zbl 0547.34041Martynyuk, A. A. 19 1984 Stability and stabilization of nonlinear systems with random structures. Zbl 1026.93002Kats, I. Ya.; Martynyuk, A. A. 19 2002 Stability theory for dynamic equations on time scales. Zbl 1359.34002Martynyuk, Anatoly A. 17 2016 Integral inequalities and stability of motion. (Интегральные неравенства и устойчивость движения.) Zbl 0462.34001Martynyuk, A. A.; Gutovski, R. 17 1979 Technical stability in dynamics. (Техническая устойчивость в динамике.) Zbl 0266.70014Martynyuk, A. A. 17 1973 Stability of motions: the role of multicomponent Liapunov’s functions. Zbl 1188.34001Martynyuk, A. A. 15 2007 Stability analysis of nonlinear systems. 2nd edition. Zbl 1405.93006Lakshmikantham, Vangipuram; Leela, Srinivasa; Martynyuk, Anatoly A. 14 2015 Qualitative methods in nonlinear dynamics: novel approaches to Liapunov’s matrix functions. Zbl 0981.93002Martynyuk, A. A. 14 2002 Stability of motion of nonautonomous systems. (Method of limiting equations) Transl. from the Russian. Zbl 0866.34046Kato, J.; Martynyuk, A. A.; Shestakov, A. A. 14 1996 Stability of motion: method of integral inequalities. Ed. and with a preface by Yu. A. Mitropol’skiĭ. (Устойчивость движения: метод интегральных неравенств.) Zbl 0751.70014Martynyuk, A. A.; Lakshmikantham, V.; Leela, S. 13 1989 Uncertain dynamical systems. Stability and motion control. Zbl 1241.37001Martynyuk, A. A.; Martynyuk-Chernienko, Yu. A. 12 2012 Elements of stability theory of A. M. Lyapunov for dynamic equations on time scales. Zbl 1133.93035Bohner, M.; Martynyuk, A. A. 11 2007 Elements of Lyapunov stability theory for dynamic equations on time-scale. Zbl 1164.34435Bohner, M.; Martynyuk, A. A. 11 2007 On application of the Lyapunov matrix-functions in the theory of stability. Zbl 0609.34057Martynyuk, A. A. 10 1985 Asymptotic stability criterion for nonlinear monotonic systems and its applications (review). Zbl 1295.93069Martynyuk, A. A. 7 2011 Uniform asymptotic stability of a singularly perturbed system via the Lyapunov matrix function. Zbl 0614.34049Martynyuk, A. A. 7 1987 Investigation of stability of large-scale systems on the basis of Lyapunov’s matrix functions. Zbl 0624.70019Martynyuk, A. A.; Shegai, V. V. 7 1986 On stability of systems with developing disturbances. Zbl 0311.34065Martynyuk, A. A. 7 1975 Bifurcations and multistability of the oscillations of a three-dimensional system. Zbl 1331.34068Martynyuk, A. A.; Nikitina, N. V. 7 2015 Stability of large-scale systems under structural and singular perturbations. (Устойчивость крупно-масштабных систем при структурных и сингулярных возмущениях.) Zbl 0582.93048Grujić, L. T.; Martynyuk, A. A.; Ribbens-Pavella, M. 6 1984 The Lyapunov matrix-function and stability of hybrid systems. Zbl 0608.34058Martynyuk, A. A. 6 1986 Motion stability of nonlinear impulsive system. Zbl 1079.34525Martynyuk, A. A.; Slyn’ko, V. I. 6 2004 Stability of solutions of autonomous Wazewski systems. Zbl 0527.34055Martynyuk, A. A.; Obolenskij, A. Yu. 6 1981 Weakly connected nonlinear systems. Boundedness and stability of motion. Zbl 1307.34002Martynyuk, Anatoly; Chernetskaya, Larisa; Martynyuk, Vladislav 6 2013 Parametric asymptotic stability of large scale systems. Zbl 1189.70085Martynyuk, A. A.; Khoroshun, A. S. 6 2008 Stability of periodic motions of quasilinear systems. Zbl 1199.34262Lila, D. M.; Martynyuk A. A. 6 2008 Setting up of the Lyapunov function for a class of systems with quasiperiodic coefficients. Zbl 1189.70084Lila, D. M.; Martynyuk, A. A. 6 2008 Technical stability of nonlinear and control systems. Zbl 0497.70040Martynyuk, A. A. 5 1979 Parametric stability of singularly perturbed nonlinear uncertain systems. Zbl 1272.70097Martynyuk, A. A.; Khoroshun, A. S. 5 2011 On stability of some solutions for equations of locked lasing of optically coupled lasers with periodic pumping. Zbl 1277.78028Lila, D. M.; Martynyuk, A. A. 5 2009 On the theory of stability of matrix differential equations. Zbl 1224.34170Lila, D. M.; Martynyuk, A. A. 5 2009 Stability in the models of real world phenomena. Zbl 1283.70006Martynyuk, A. A. 5 2011 Stability theorems in impulsive functional differential equations with infinite delay. Zbl 1047.34087Martynyuk, A. A.; Shen, J. H.; Stavroulakis, I. P. 5 2003 On the stability of analytic motions. Zbl 0238.34087Martynyuk, A. A. 5 1972 Qualitative analysis of set-valued differential equations. Zbl 1428.49002Martynyuk, Anatoly A. 5 2019 On periodic motions in three-dimensional systems. Zbl 1331.34023Martynyuk, A. A.; Nikitina, N. V. 5 2015 Elements of the theory of stability of hybrid systems (review). Zbl 1331.93001Martynyuk, A. A. 5 2015 Stability and bifurcation in a model of the magnetic field of the earth. Zbl 1314.86008Martynyuk, A. A.; Nikitina, N. B. 4 2014 Development of instability in a rotating elastoplastic annular disk. Zbl 1295.74031Lila, D. M.; Martynyuk, A. A. 4 2012 The Lyapunov matrix function and the stability of hybrid systems. Zbl 0597.70022Martynyuk, A. A. 4 1985 On the theory of Lyapunov’s direct method. Zbl 1327.34100Martynyuk, A. A. 4 2006 On periodic motion and bifurcations in three-dimensional nonlinear systems. Zbl 1345.37016Martynyuk, A. A.; Nikitina, N. V. 4 2015 Stability results for large-scale difference systems via matrix-valued Liapunov functions. Zbl 1132.39006Martynyuk, A. A.; Slyn’ko, V. I. 4 2007 Novel qualitative methods of nonlinear mechanics and their application to the analysis of multifrequency oscillations, stability, and control problems. Zbl 1177.93002Kovalev, A. M.; Martynyuk, A. A.; Boichuk, O. A.; Mazko, A. G.; Petryshyn, R. I.; Slyusarchuk, V. Yu.; Zuyev, A. L.; Slyn’ko, V. I. 4 2009 Stability theory of solutions of dynamic equations on time scales. (Теория устойчивости решений динамических уравнений на временной шкале.) Zbl 1262.34002Martynyuk, A. A. 4 2012 Probabilistic estimates for solutions of a linear system of differential equations with stochastic coefficients. Zbl 0232.60030Kirichenko, N. F.; Martynyuk, A. A. 4 1972 Constructive estimation of the Lyapunov function for quadratic nonlinear systems. Zbl 1397.70031Martynyuk, A. A.; Khusainov, D. Ya.; Chernienko, V. A. 4 2018 Fractional-like derivative of Lyapunov-type functions and applications to stability analysis of motion. Zbl 1387.34007Martynyuk, Anatoliy A.; Stamova, Ivanka M. 4 2018 Practical stability of a moving robot with respect to given domains. Zbl 1294.70006Martynyuk, À. À.; Khoroshun, À. S.; Chernienko, À. N. 3 2014 Stabilization of the motion of pseudo-linear affine systems. Zbl 1375.93103Martynyuk, A. A.; Chernetskaya, L. N.; Martynyuk-Chernienko, Yu. A. 3 2017 On some directions of V. Laksmikantham investigations on the theory of differential equations and their applications. Zbl 0633.34001Mitropol’skij, Yu. A.; Lila, S.; Martynyuk, A. A. 3 1986 Method of the application of matrix functions in stability theory. Zbl 0664.70032Martynyuk, A. A.; Krapivnyi, Yu. N. 3 1988 Methods and problems of the practical stability of motion theory. Zbl 0569.34046Martynyuk, A. A. 3 1984 Motion stability in a case that is close to the critical one. Zbl 0581.70018Martynyuk, A. A.; Nikitina, N. V. 3 1985 Stability of nonlinear systems under structural perturbations. Zbl 1330.34011Martynyuk, A. A.; Miladzhanov, V. G. 3 2015 On the theory of parametric stability. Zbl 1150.34494Martynyuk, A. A.; Khoroshun, A. S. 3 2007 Stability analysis by comparison technique. Zbl 1095.34032Martynyuk, A. A. 3 2005 Stability of dynamical systems in metric space. Zbl 1088.34056Martynyuk, A. A. 3 2005 Block-diagonal matrix Lyapunov function and stability of uncertain impulsive system. Zbl 1079.34524Martynyuk, A. A. 3 2004 Analysis of stability problems via matrix Lyapunov functions. Zbl 0714.34082Martynyuk, Anatoly A. 3 1990 Advances in stability theory at the end of the 20th century. Zbl 1020.00004 3 2003 Analysis of the trajectory set of nonlinear dynamics: estimates of solutions and comparison principle. Zbl 1266.34029Martynyuk, A. A.; Martynyuk-Chernienko, Yu. A. 3 2012 Construction of solutions of systems of differential equations in the region of asymptotic stability. Zbl 0209.39403Martynyuk, A. A. 3 1970 Practical stability analysis with respect to manifolds and boundedness of differential equations with fractional-like derivatives. Zbl 1481.34069Martynyuk, Anatoliy; Stamov, Gani; Stamova, Ivanka 3 2019 Integral estimates of the solutions of fractional-like equations of perturbed motion. Zbl 1426.34015Martynyuk, Anatoliy; Stamov, Gani; Stamova, Ivanka 3 2019 Revisiting the theory of stability over a finite interval. Zbl 1314.70044Martynyuk, A. A.; Khoroshun, A. S. 2 2014 Revisiting the theory of stability of stationary linear large-scale systems. Zbl 1295.93060Martynyuk, A. A.; Mullazhonov, R. V. 2 2012 Uniform asymptotic stability of a singularly perturbed system on the basis of the Lyapunov matrix function. Zbl 0611.34047Martynyuk, A. A. 2 1986 Limiting equations and stability of non-stationary motions. Zbl 0651.34047Martynyuk, A. A.; Karimzhanov, A. 2 1988 Stability of processes under continuous and discrete perturbations. (Ustojchivost’ protsessov pri nepreryvnykh i diskretnykh vozmushcheniyakh). With a foreword by A. A. Martynyuk. (Ustojchivost’ protsessov pri nepreryvnykh i diskretnykh vozmushcheniyakh.) Zbl 0708.34045Borisenko, S. D.; Kosolapov, V. I.; Obolenskij, A. Yu. 2 1988 Investigation of the stability of singularly perturbed autonomous systems by means of matrix Lyapunov functions. Zbl 0673.34058Martynyuk, A. A.; Miladzhanov, V. G. 2 1988 On Lyapunov stability of impulsive Takagi-Sugeno fuzzy systems. Zbl 1277.93059Denisenko, V. S.; Martynyuk, A. A.; Slyn’ko, V. I. 2 2008 Stability in singularly perturbed systems with structural perturbations. Some applications. Zbl 1121.93312Martynyuk, A. A.; Miladzhanov, V. G. 2 2003 Method of decomposing large-scale systems in a study of stability of motion. Zbl 0683.70023Krapivnyj, Yu. N.; Martynyuk, A. A. 2 1988 A hierarchical matrix Lyapunov function and stability under structural perturbations. Zbl 0701.34063Martynyuk, A. A. 2 1989 A survey of collected works of V. Lakshmikantham. Zbl 0712.34014Leela, S.; Mitropol’skij, Yu. A.; Martynyuk, A. A. 2 1986 Hierarchical matrix Lyapunov function. Zbl 0716.34056Martynyuk, A. A. 2 1989 Nikolai Alekseevich Izobov (a tribute in honor of his 70th birthday). Zbl 1191.01030Arutyunov, A. V.; Bibikov, Yu. N.; Emel’yanov, S. V.; Gaishun, I. V.; Il’in, V. A.; Kiguradze, I. T.; Korovin, S. K.; Kudryavtsev, L. D.; Kurzhanskii, A. B.; Makarov, E. K.; Martynyuk, A. A.; Mazanik, S. A.; Mishchenko, E. F.; Moiseev, E. I.; Osipov, Yu. S.; Pliss, V. A.; Rozov, N. Kh.; Sadovnichii, V. A.; Samoilenko, A. M.; Shemyakina, T. K.; Vasil’ev, F. P. 2 2010 A survey of some classical and modern developments of stability theory. Zbl 0956.34040Martynyuk, A. A. 2 2000 Qualitative and numerical-analytical investigation of the stability of motion. Zbl 0395.70009Martynyuk, A. A. 2 1977 Decomposition and aggregation in the analysis of systems. Zbl 0435.70011Martynyuk, A. 2 1975 A generalization of the second theorem of N. N. Bogolyubov’s averaging principle. Zbl 0448.34049Martynyuk, A. A. 2 1979 Construction and applications of the matrix-valued Liapunov functions for some quasi-periodic systems. Zbl 1207.34067Lila, D. M.; Martynyuk, A. A. 2 2009 Qualitative analysis of nonlinear systems by the method of matrix Lyapunov functions. Zbl 0841.34057Martynyuk, A. A. 2 1995 Boundedness criteria for solutions of perturbed Kolmogorov population models. Zbl 0844.92018Freedman, H. I.; Martynyuk, A. A. 2 1995 Stability analysis: nonlinear mechanics equations. Transl. from the Russian by Svetlana Raschivalova. Zbl 0840.34003Martynyuk, A. A. 2 1995 Integro-differential inequalities in the theory of stability of motion. Zbl 0342.34036Martynyuk, A. A. 2 1976 On a comparison method in the problem of continuous dependence on the parameter. Zbl 0513.34005Martynyuk, A. A. 2 1982 Nonlinear comparison systems in stability problems of large-scale systems. Zbl 0513.70026Martynyuk, A. A.; Nikitina, N. V. 2 1981 On the exponential stability of a dynamical system on a time scale. Zbl 1234.34056Martynyuk, A. A. 2 2008 Nonlinear dynamic inequalities and stability of quasilinear systems on time scales. Zbl 1298.34172Babenko, S. V.; Martynyuk, A. A. 2 2013 On the connective stability of impulsive large-scale systems with delay. Zbl 1265.34266Martynyuk, A. A.; Ivanov, I. L. 2 2012 On the robust stability of impulsive systems with delay. Zbl 1265.34267Martynyuk, A. A.; Martynyuk-Chernienko, Yu. A. 2 2012 On the stabilization of the motion of hybrid systems with aftereffect. Zbl 1265.74045Martynyuk, A. A. 2 2012 Sufficient stability conditions for polynomial systems. Zbl 1441.37040Martynyuk, A. A.; Chernienko, V. A. 2 2020 Qualitative analysis of set-valued differential equations. Zbl 1428.49002Martynyuk, Anatoly A. 5 2019 Practical stability analysis with respect to manifolds and boundedness of differential equations with fractional-like derivatives. Zbl 1481.34069Martynyuk, Anatoliy; Stamov, Gani; Stamova, Ivanka 3 2019 Integral estimates of the solutions of fractional-like equations of perturbed motion. Zbl 1426.34015Martynyuk, Anatoliy; Stamov, Gani; Stamova, Ivanka 3 2019 Stability of sets of hybrid dynamical systems with aftereffect. Zbl 1435.34066Martynyuk, A. A.; Stamova, I. M. 2 2019 Constructive estimation of the Lyapunov function for quadratic nonlinear systems. Zbl 1397.70031Martynyuk, A. A.; Khusainov, D. Ya.; Chernienko, V. A. 4 2018 Fractional-like derivative of Lyapunov-type functions and applications to stability analysis of motion. Zbl 1387.34007Martynyuk, Anatoliy A.; Stamova, Ivanka M. 4 2018 On the stability of solutions of fractional-like equations of perturbed motion. Zbl 1413.70015Martynyuk, A. A. 2 2018 On a development of the comparison principle in the stability theory of motion. Zbl 1417.34079Martynyuk, Anatoliy; Stamov, Gani; Stamova, Ivanka 1 2018 Stabilization of the motion of pseudo-linear affine systems. Zbl 1375.93103Martynyuk, A. A.; Chernetskaya, L. N.; Martynyuk-Chernienko, Yu. A. 3 2017 Robust stabilization of bilinear systems under interval initial conditions. Zbl 1398.93282Martynyuk, A. A.; Babenko, E. A. 2 2017 Analysis of a set of trajectories of generalized standard systems: averaging technique. Zbl 1373.34076Martynyuk, A. A. 1 2017 Constructive estimates of Lyapunov \(V\)-function for perturbed equations of motion. Zbl 1381.93092Martynyuk, A. A. 1 2017 Comparison principle based on Minkowski mixed volumes for a family of differential equations. Zbl 1393.34031Martynyuk, A. A. 1 2017 Stability theory for dynamic equations on time scales. Zbl 1359.34002Martynyuk, Anatoly A. 17 2016 Integral estimates of solutions to nonlinear systems and their applications. Zbl 1343.34131Martynyuk, A. A.; Khusainov, D. Ya.; Chernienko, V. A. 2 2016 Stabilization of the motion of affine systems. Zbl 1382.93025Babenko, E. A.; Martynyuk, A. A. 2 2016 On the stability of a system of equations with fractional derivatives with respect to two measures. Zbl 1425.34071Martynyuk, A. A. 1 2016 Dwell time stability analysis for nonlinear switched difference systems. Zbl 1359.39008Aleksandrov, A. Yu.; Martynyuk, A. A.; Platonov, A. V. 1 2016 Stability analysis of nonlinear systems. 2nd edition. Zbl 1405.93006Lakshmikantham, Vangipuram; Leela, Srinivasa; Martynyuk, Anatoly A. 14 2015 Bifurcations and multistability of the oscillations of a three-dimensional system. Zbl 1331.34068Martynyuk, A. A.; Nikitina, N. V. 7 2015 On periodic motions in three-dimensional systems. Zbl 1331.34023Martynyuk, A. A.; Nikitina, N. V. 5 2015 Elements of the theory of stability of hybrid systems (review). Zbl 1331.93001Martynyuk, A. A. 5 2015 On periodic motion and bifurcations in three-dimensional nonlinear systems. Zbl 1345.37016Martynyuk, A. A.; Nikitina, N. V. 4 2015 Stability of nonlinear systems under structural perturbations. Zbl 1330.34011Martynyuk, A. A.; Miladzhanov, V. G. 3 2015 Analysis of the set of trajectories of nonlinear dynamics: equations with causal robust operator. Zbl 1322.34027Martynyuk, A. A.; Martynyuk-Chernienko, Yu. A. 1 2015 Qualitative analysis of singularly perturbed Takagi-Sugeno systems: the case of unstable subsystems. Zbl 1327.34088Khoroshun, A. S.; Martynyuk, A. A. 1 2015 Analysis of a set of nonlinear dynamics trajectories: stability of difference equations. Zbl 1297.39019Aleksandrov, A. Yu.; Martynyuk, A. A.; Platonov, A. V. 1 2015 Stability and bifurcation in a model of the magnetic field of the earth. Zbl 1314.86008Martynyuk, A. A.; Nikitina, N. B. 4 2014 Practical stability of a moving robot with respect to given domains. Zbl 1294.70006Martynyuk, À. À.; Khoroshun, À. S.; Chernienko, À. N. 3 2014 Revisiting the theory of stability over a finite interval. Zbl 1314.70044Martynyuk, A. A.; Khoroshun, A. S. 2 2014 On the stability of motion with respect to two measures for systems with aftereffect and impulsive perturbations. Zbl 1317.34164Martynyuk, A. A. 1 2014 Stability of controlled systems with two controls on the time scale. Zbl 1304.34157Babenko, S. V.; Martynyuk, A. A. 1 2014 Stability of dynamic graph on time scales. Zbl 1304.34158Babenko, S. V.; Martynyuk, A. A. 1 2014 Weakly connected nonlinear systems. Boundedness and stability of motion. Zbl 1307.34002Martynyuk, Anatoly; Chernetskaya, Larisa; Martynyuk, Vladislav 6 2013 Nonlinear dynamic inequalities and stability of quasilinear systems on time scales. Zbl 1298.34172Babenko, S. V.; Martynyuk, A. A. 2 2013 Analysis of the set of trajectories of nonlinear dynamics: stability and boundedness of motions. Zbl 1277.34073Martynyuk, A. A.; Martynyuk-Chernienko, Yu. A. 2 2013 Direct Lyapunov method on time scales. Zbl 1307.34137Martynyuk, A. A. 1 2013 Sufficient conditions of connective stability of motion on time scale. Zbl 1272.34123Luk’yanova, T. A.; Martynyuk, A. A. 1 2013 On the stability of a motion under interval initial conditions. Zbl 1289.34135Martynyuk, A. A. 1 2013 On the connective stability of three-machine energetic system with impulsive disturbances. Zbl 1289.70010Martynyuk, A. A.; Ivanov, I. L. 1 2013 On the instability of motion under interval initial data. Zbl 1289.93103Martynyuk, A. A. 1 2013 Uncertain dynamical systems. Stability and motion control. Zbl 1241.37001Martynyuk, A. A.; Martynyuk-Chernienko, Yu. A. 12 2012 Development of instability in a rotating elastoplastic annular disk. Zbl 1295.74031Lila, D. M.; Martynyuk, A. A. 4 2012 Stability theory of solutions of dynamic equations on time scales. (Теория устойчивости решений динамических уравнений на временной шкале.) Zbl 1262.34002Martynyuk, A. A. 4 2012 Analysis of the trajectory set of nonlinear dynamics: estimates of solutions and comparison principle. Zbl 1266.34029Martynyuk, A. A.; Martynyuk-Chernienko, Yu. A. 3 2012 Revisiting the theory of stability of stationary linear large-scale systems. Zbl 1295.93060Martynyuk, A. A.; Mullazhonov, R. V. 2 2012 On the connective stability of impulsive large-scale systems with delay. Zbl 1265.34266Martynyuk, A. A.; Ivanov, I. L. 2 2012 On the robust stability of impulsive systems with delay. Zbl 1265.34267Martynyuk, A. A.; Martynyuk-Chernienko, Yu. A. 2 2012 On the stabilization of the motion of hybrid systems with aftereffect. Zbl 1265.74045Martynyuk, A. A. 2 2012 Stability of motion of nonlinear systems with fuzzy characteristics of parameters. Zbl 1263.34008Martynyuk, A. A.; Martynyuk-Chernienko, Yu. A. 2 2012 On instability of a rotating elastoplastic composite plane circular disc. Zbl 1274.74136Lila, D. M.; Martynyuk, A. A. 2 2012 Asymptotic stability criterion for nonlinear monotonic systems and its applications (review). Zbl 1295.93069Martynyuk, A. A. 7 2011 Parametric stability of singularly perturbed nonlinear uncertain systems. Zbl 1272.70097Martynyuk, A. A.; Khoroshun, A. S. 5 2011 Stability in the models of real world phenomena. Zbl 1283.70006Martynyuk, A. A. 5 2011 About the stability loss of a rotating elastoplastic circular disc. Zbl 1230.74044Lula, D. M.; Martynyuk, A. A. 1 2011 Uncertain dynamical systems. Stability and motion control. Transl. from the English. Zbl 1248.37003Martynyuk, A. A.; Martynyuk-Chernienko, Yu. A.; Sun, Zhen Qi 1 2011 On the asymptotic stability of a neural network on a time scale. Zbl 1334.34195Luk’yanova, T. A.; Martynyuk, A. A. 1 2011 Nikolai Alekseevich Izobov (a tribute in honor of his 70th birthday). Zbl 1191.01030Arutyunov, A. V.; Bibikov, Yu. N.; Emel’yanov, S. V.; Gaishun, I. V.; Il’in, V. A.; Kiguradze, I. T.; Korovin, S. K.; Kudryavtsev, L. D.; Kurzhanskii, A. B.; Makarov, E. K.; Martynyuk, A. A.; Mazanik, S. A.; Mishchenko, E. F.; Moiseev, E. I.; Osipov, Yu. S.; Pliss, V. A.; Rozov, N. Kh.; Sadovnichii, V. A.; Samoilenko, A. M.; Shemyakina, T. K.; Vasil’ev, F. P. 2 2010 Professor V.I. Zubov. Zbl 1300.34003Aleksandrov, A. Yu.; Martynyuk, A. A.; Zhabko, A. P. 1 2010 On the stability of a neural network on the time scale. Zbl 1199.93239Martynyuk, A. A.; Luk’yanova, T. A. 1 2010 On the Lyapunov direct method for equations with fractional derivatives. Zbl 1224.34172Martynyuk, A. A. 1 2010 On a mathematical model of world dynamics and sustainable development. Zbl 1224.91111Martynyuk, A. A. 1 2010 On stability of Hopfield neural network on time scales. Zbl 1344.34099Martynyuk, A. A.; Lukyanova, T. A.; Rasshyvalova, S. N. 1 2010 Integral inequalities and stability of an equilibrium state on a time scale. Zbl 1240.93267Luk’yanova, T. A.; Martynyuk, A. A. 1 2010 On stability of some solutions for equations of locked lasing of optically coupled lasers with periodic pumping. Zbl 1277.78028Lila, D. M.; Martynyuk, A. A. 5 2009 On the theory of stability of matrix differential equations. Zbl 1224.34170Lila, D. M.; Martynyuk, A. A. 5 2009 Novel qualitative methods of nonlinear mechanics and their application to the analysis of multifrequency oscillations, stability, and control problems. Zbl 1177.93002Kovalev, A. M.; Martynyuk, A. A.; Boichuk, O. A.; Mazko, A. G.; Petryshyn, R. I.; Slyusarchuk, V. Yu.; Zuyev, A. L.; Slyn’ko, V. I. 4 2009 Construction and applications of the matrix-valued Liapunov functions for some quasi-periodic systems. Zbl 1207.34067Lila, D. M.; Martynyuk, A. A. 2 2009 On instability of solutions of dynamic equations on time scales. Zbl 1199.34479Martynyuk, A. A. 1 2009 Advances in chaotic dynamics and applictions. Zbl 1188.37004 1 2009 Parametric asymptotic stability of large scale systems. Zbl 1189.70085Martynyuk, A. A.; Khoroshun, A. S. 6 2008 Stability of periodic motions of quasilinear systems. Zbl 1199.34262Lila, D. M.; Martynyuk A. A. 6 2008 Setting up of the Lyapunov function for a class of systems with quasiperiodic coefficients. Zbl 1189.70084Lila, D. M.; Martynyuk, A. A. 6 2008 On Lyapunov stability of impulsive Takagi-Sugeno fuzzy systems. Zbl 1277.93059Denisenko, V. S.; Martynyuk, A. A.; Slyn’ko, V. I. 2 2008 On the exponential stability of a dynamical system on a time scale. Zbl 1234.34056Martynyuk, A. A. 2 2008 Oscillations of conservative systems with complex trajectories. Zbl 1199.34233Martynyuk, A. A.; Nikitina, N. V. 2 2008 A general problem of the polydynamics on the time scale. Zbl 1150.93523Martynyuk, A. A. 1 2008 On the principle of comparison for a system of matrix differential equations. Zbl 1164.93396Martynyuk, A. A. 1 2008 On stability of linear hybrid mechanical systems with distributed components. Zbl 1164.70340Martynyuk, A. A.; Slyn’ko, V. I. 1 2008 Chaotic motions of systems with dry friction. Zbl 1199.34205Martynyuk, A. A.; Nikitina, N. V. 1 2008 On a nonlinear inequality on the time scale. Zbl 1194.26034Martynyuk, A. A.; Slyn’ko, V. I. 1 2008 Stability of motions: the role of multicomponent Liapunov’s functions. Zbl 1188.34001Martynyuk, A. A. 15 2007 Elements of stability theory of A. M. Lyapunov for dynamic equations on time scales. Zbl 1133.93035Bohner, M.; Martynyuk, A. A. 11 2007 Elements of Lyapunov stability theory for dynamic equations on time-scale. Zbl 1164.34435Bohner, M.; Martynyuk, A. A. 11 2007 Stability results for large-scale difference systems via matrix-valued Liapunov functions. Zbl 1132.39006Martynyuk, A. A.; Slyn’ko, V. I. 4 2007 On the theory of parametric stability. Zbl 1150.34494Martynyuk, A. A.; Khoroshun, A. S. 3 2007 On the construction of a matrix-valued Lyapunov function for a linear periodic system on a time scale. Zbl 1158.34331Martynyuk, A. A.; Slyn’ko, V. I. 1 2007 Stability of a set of trajectories of nonlinear dynamics. Zbl 1168.34340Martynyuk, A. A. 1 2007 On the polydynamics of nonlinear systems on a time scale. Zbl 1157.39309Martynyuk, A. A. 1 2007 On the theory of Lyapunov’s direct method. Zbl 1327.34100Martynyuk, A. A. 4 2006 Stability analysis by comparison technique. Zbl 1095.34032Martynyuk, A. A. 3 2005 Stability of dynamical systems in metric space. Zbl 1088.34056Martynyuk, A. A. 3 2005 Investigation of composite oscillations. Zbl 1099.34514Martynyuk, A. A.; Nikitina, N. V. 1 2005 Complex behavior of a trajectory in two- and one-frequency systems. Zbl 1089.70520Martynyuk, A. A.; Nikitina, N. V. 1 2005 On the boundedness of motions of mechanical systems described by fuzzy ordinary differential equations. Zbl 1114.34311Martynyuk, A. A.; Slyn’ko, V. I. 1 2005 Motion stability of nonlinear impulsive system. Zbl 1079.34525Martynyuk, A. A.; Slyn’ko, V. I. 6 2004 Block-diagonal matrix Lyapunov function and stability of uncertain impulsive system. Zbl 1079.34524Martynyuk, A. A. 3 2004 Matrix Liapunov’s functions method and stability analysis of continuous systems. Zbl 1091.34030Martynyuk, A. A. 2 2004 Matrix-valued functionals approach for stability analysis of functional differential equations. Zbl 1046.34087Martynyuk, A. A. 1 2004 ...and 92 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 797 Authors 103 Martynyuk, Anatoliĭ Andriĭovych 27 Gumel, Abba B. 22 Stamova, Ivanka Milkova 14 Martynyuk-Chernienko, Yu. A. 14 Slyn’ko, Vitalii Ivanovich 13 Aleksandrov, Aleksandr Yur’evich 12 Khoroshun, A. S. 12 Lakshmikantham, Vangipuram 11 Nikitina, Nelly Vladimirovna 10 Leela, Srinivasa G. 10 Lila, D. M. 10 Sharomi, Oluwaseun Y. 9 Agarwal, Ravi P. 9 Stamov, Gani Trendafilov 8 Agusto, Folashade B. 8 Okuonghae, Daniel 8 Platonov, Alekseĭ Viktorovich 8 Slyusarchuk, Vasyl Yukhimovich 8 Tiwari, Pankaj Kumar 7 Bowong, Samuel 7 Liu, Xinzhi 6 Bainov, Drumi Dimitrov 6 Li, An 6 Medina, Rigoberto 6 Podder, Chandra Nath 5 Chernetskaya, Larisa Nikolaevna 5 Defoort, Michael 5 Djemai, Mohamed 5 Grujić, Ljubomir T. 5 Hove-Musekwa, Senelani Dorothy 5 Jiang, Guoping 5 Khristova, Snezhana G. 5 Tchuenche, Jean Michel 5 Vorotnikov, V. I. 5 Yakar, Coskun 4 Chattopadhyay, Joydev 4 Chernienko, V. A. 4 Denisenko, V. S. 4 Dvirny, Aleksandr Ivanovich 4 Hammami, Mohamed Ali 4 Huo, Hai-Feng 4 Lü, Xiaodong 4 Lungu, Nicolaie 4 Matvijchuk, K. S. 4 Mukandavire, Zindoga 4 O’Regan, Donal 4 Pal, Samaresh 4 Pichkur, Volodymyr V. 4 Sangaré, Boureima 4 Song, Xinyu 4 Traoré, Bakary 4 Zhang, Yi 3 Baker, Christopher Thomas Hale 3 Borysenko, S. D. 3 Boukas, El-Kébir 3 Boukerrioua, Khaled 3 Chen, Guanrong 3 Çiçek, Muhammed 3 de León, Jesús Ponce 3 Elbasha, Elamin H. 3 Ghanmi, Boulbaba 3 Ghosh, Mini 3 Gücen, Mustafa Bayram 3 Haddad, Wassim Michael 3 Hussaini, Nafiu 3 Iovane, Gerardo 3 Kang, Yun 3 Karimzhanov, A. 3 Koutou, Ousmane 3 Kurths, Jürgen 3 Mbang, Joseph 3 Misra, Arvind Kumar 3 Mytropol’skyĭ, Yuriĭ Oleksiĭovych 3 Sivasundaram, Seenith 3 Sun, Ji Tao 3 Tang, Wallace Kit-Sang 3 Vasundhara Devi, Jonnalagadda 3 Zhang, Xianfu 2 Ahmad, Bashir 2 Al-saedi, Ahmed Eid Salem 2 Alsaleh, Aliya A. 2 Anabtawi, M. J. 2 Babenko, Ekaterina A. 2 Babenko, Sergei V. 2 Bai, Zhenguo 2 Ben Nasser, Bacem 2 Benhadj Braiek, Naceur 2 Benner, Peter 2 Bohner, Martin J. 2 Bouafoura, Mohamed Karim 2 Che, Yan 2 Chinviriyasit, Settapat 2 Chinviriyasit, Wirawan 2 Chiu, Kuo-Shou 2 Chu, Tianguang 2 Ciplea, Sorina Anamaria 2 Clempner, Julio B. 2 Cruz-Hernández, César 2 Das, Prasenjit 2 Denysenko, V. S. ...and 697 more Authors all top 5 Cited in 143 Serials 59 International Applied Mechanics 32 Soviet Applied Mechanics 28 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 25 Applied Mathematics and Computation 22 Journal of Mathematical Analysis and Applications 21 Ukrainian Mathematical Journal 16 Automation and Remote Control 16 Nonlinear Analysis. Hybrid Systems 16 Nonlinear Analysis. Theory, Methods & Applications 14 Chaos, Solitons and Fractals 12 Automatica 12 Journal of Mathematical Sciences (New York) 12 Nonlinear Dynamics 12 Differential Equations 10 Mathematical Biosciences 10 Advances in Difference Equations 9 International Journal of Control 9 Journal of the Franklin Institute 9 Systems & Control Letters 9 Doklady Mathematics 9 Nonlinear Analysis. 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Serie II 1 Revista Colombiana de Matemáticas 1 Ricerche di Matematica 1 Theoretical Computer Science 1 Theoretical Population Biology 1 Tohoku Mathematical Journal. Second Series 1 Transactions of the American Mathematical Society 1 Moscow University Computational Mathematics and Cybernetics 1 Circuits, Systems, and Signal Processing 1 Acta Applicandae Mathematicae 1 Journal of the Nigerian Mathematical Society 1 MCSS. 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