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## Akhmet, Marat Ubaydulla

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 Author ID: akhmet.marat-u Published as: Akhmet, M.; Akhmet, M. U.; Akhmet, Marat; Akhmet, Marat U.; Akhmet, Marat U.; Akhmetov, M.; Akhmetov, M. U. Homepage: http://users.metu.edu.tr/marat/ External Links: MGP · Wikidata · ORCID · ResearchGate · dblp
 Documents Indexed: 158 Publications since 1983, including 7 Books Reviewing Activity: 69 Reviews
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#### Co-Authors

 35 single-authored 25 Perestyuk, Mykola Oleksiĭovych 24 Fen, Mehmet Onur 9 Zafer, Ağacık 8 Aruğaslan, Duygu 8 Yılmaz, Enes 7 Kashkynbayev, Ardak 7 Kivilcim, Ayşegül 7 Turan, Mehmet 6 Tleubergenova, M. A. 3 Alejaily, Ejaily Milad 3 Alzabut, Jehad O. 3 Büyükadalı, C. 3 Çağ, Sabahattin 3 Ergenç, Tanil 3 Tleubergenova, Madina 3 Zhamanshin, Akylbek 2 Beklioglu, M. 2 Bekmukhambetova, G. A. 2 Liu, Xinzhi 2 Seilova, R. D. 2 Sejilova, R. D. 2 Uğur, Ömür 2 Weber, Gerhard-Wilhelm 1 Akalin, E. 1 Aklain, E. 1 Altıntan, Derya 1 Alwan, Mohamad S. 1 Aruğaslan Çinçin, Duygu 1 Bekmukhambetova, Gul’baram 1 Cengiz, Nur 1 Dauylbaev, Murathan 1 Fečkan, Michal 1 Gebert, Jutta 1 Karacaören, M. 1 Kirane, Mukhtar Bin Muhammad 1 Mehmet, Onur Fen 1 Mirzakulova, Aziza 1 Nagaev, R. F. 1 Öktem, Hakan 1 Pickl, Stefan Wolfgang 1 Rafatov, Ismail R. 1 Sal’zhanova, M. B. 1 Seilova, Roza 1 Serinağaoğlu, Y. 1 Tkachenko, Victor Ivanovich 1 Tleubergenov, M. A. 1 Yilmaz, Oguz 1 Yilmaz, Ozlem
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#### Serials

 12 Ukrainian Mathematical Journal 12 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 10 Communications in Nonlinear Science and Numerical Simulation 8 Ukraïns’kyĭ Matematychnyĭ Zhurnal 8 Discontinuity, Nonlinearity, and Complexity 6 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 5 Journal of Mathematical Analysis and Applications 4 Computers & Mathematics with Applications 4 Turkish Journal of Mathematics 4 Electronic Journal of Qualitative Theory of Differential Equations 4 Dynamics of Continuous, Discrete & Impulsive Systems. Series A. Mathematical Analysis 4 Miskolc Mathematical Notes 3 Izvestiya Akademii Nauk Kazakhskoĭ SSR, Seriya Fiziko-Matematicheskaya 3 Journal of Computational and Applied Mathematics 3 Applied Mathematics Letters 3 Chaos 3 Nonlinear Analysis. Real World Applications 3 Nonlinear Analysis. Hybrid Systems 3 Nonlinear Systems and Complexity 2 Doklady Akademii Nauk Ukrainskoĭ SSR, Seriya A 2 Differential Equations 2 Neural Networks 2 Nonlinear Studies 2 Nonlinear Dynamics 2 Neliniĭni Kolyvannya 2 Differential Equations 2 International Journal of Qualitative Theory of Differential Equations and Applications 2 Nonlinear Physical Science 1 Journal of Applied Mathematics and Mechanics 1 Applied Mathematics and Computation 1 Differentsial’nye Uravneniya 1 Journal of Optimization Theory and Applications 1 Mathematics and Computers in Simulation 1 Dynamic Systems and Applications 1 European Journal of Operational Research 1 Studia Universitatis Babeş-Bolyai. Mathematica 1 Journal of Nonlinear Science 1 Discrete and Continuous Dynamical Systems 1 Communications in Applied Analysis 1 Differential Equations and Dynamical Systems 1 Vychislitel’nye Tekhnologii 1 Visnyk Kyïvs’kogo Universytetu. Matematyka i Mekhanika 1 Dynamics of Continuous, Discrete & Impulsive Systems. Series B. Applications & Algorithms 1 Discrete and Continuous Dynamical Systems. Series B 1 Communications on Pure and Applied Analysis 1 Carpathian Journal of Mathematics 1 Matematicheskiĭ Zhurnal 1 Matematicheskaya Fizika 1 Atlantis Studies in Mathematics for Engineering and Science 1 Nonlinear Analysis. Theory, Methods & Applications 1 Applied Mathematics and Nonlinear Sciences
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#### Fields

 135 Ordinary differential equations (34-XX) 42 Dynamical systems and ergodic theory (37-XX) 28 Biology and other natural sciences (92-XX) 14 Systems theory; control (93-XX) 7 Mechanics of particles and systems (70-XX) 5 Difference and functional equations (39-XX) 4 Partial differential equations (35-XX) 4 Computer science (68-XX) 3 Integral equations (45-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Fluid mechanics (76-XX) 1 General and overarching topics; collections (00-XX) 1 Measure and integration (28-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Operator theory (47-XX) 1 General topology (54-XX) 1 Statistics (62-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Operations research, mathematical programming (90-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

#### Citations contained in zbMATH Open

113 Publications have been cited 899 times in 415 Documents Cited by Year
Principles of discontinuous dynamical systems. Zbl 1204.37002
Akhmet, Marat
2010
An impulsive ratio-dependent predator-prey system with diffusion. Zbl 1114.35097
Akhmet, M. U.; Beklioglu, M.; Ergenc, T.; Tkachenko, V. I.
2006
Integral manifolds of differential equations with piecewise constant argument of generalized type. Zbl 1122.34054
Akhmet, M. U.
2007
Stability of differential equations with piecewise constant arguments of generalized type. Zbl 1173.34042
Akhmet, M. U.
2008
On the reduction principle for differential equations with piecewise constant argument of generalized type. Zbl 1134.34048
Akhmet, M. U.
2007
On the general problem of stability for impulsive differential equations. Zbl 1047.34094
Akhmet, M. U.
2003
Nonlinear hybrid continuous/discrete-time models. Zbl 1328.93001
Akhmet, Marat
2011
Perturbations and Hopf bifurcation of the planar discontinuous dynamical system. Zbl 1066.34008
Akhmet, M. U.
2005
The differential equations on time scales through impulsive differential equations. Zbl 1110.34006
Akhmet, M. U.; Turan, M.
2006
Stability in cellular neural networks with a piecewise constant argument. Zbl 1191.68484
Akhmet, M. U.; Aruğaslan, D.; Yılmaz, E.
2010
Impulsive Hopfield-type neural network system with piecewise constant argument. Zbl 1202.92001
Akhmet, M. U.; Yılmaz, E.
2010
Li-Yorke chaos in the system with impacts. Zbl 1153.37017
Akhmet, M. U.
2009
Perron’s theorem for linear impulsive differential equations with distributed delay. Zbl 1101.34065
Akhmet, M. U.; Alzabut, J.; Zafer, A.
2006
Stability analysis of recurrent neural networks with piecewise constant argument of generalized type. Zbl 1400.34112
Akhmet, M. U.; Aruğaslan, D.; Yılmaz, E.
2010
Periodic and almost periodic solutions of strongly nonlinear impulsive systems. Zbl 0791.34034
Akhmetov, M. U.; Perestyuk, N. A.
1992
Devaney’s chaos of a relay system. Zbl 1221.37030
Akhmet, M. U.
2009
Lyapunov-Razumikhin method for differential equations with piecewise constant argument. Zbl 1179.34077
Akhmet, Marat; Aruğaslan, Duygu
2009
Chaotic period-doubling and OGY control for the forced Duffing equation. Zbl 1253.34048
Akhmet, M. U.; Fen, M. O.
2012
Almost periodic solutions of differential equations with piecewise constant argument of generalized type. Zbl 1166.34039
Akhmet, M. U.
2008
Dynamical synthesis of quasi-minimal sets. Zbl 1176.34009
Akhmet, M. U.
2009
A comparison method for differential equations with impulse actions. Zbl 0726.34010
Akhmetov, M. U.; Perestyuk, N. A.
1990
Differential equations with state-dependent piecewise constant argument. Zbl 1195.34103
Akhmet, M. U.; Büyükadalı, C.
2010
Asymptotic behavior of solutions of differential equations with piecewise constant arguments. Zbl 1152.34348
Akhmet, M. U.
2008
Differential equations on variable time scales. Zbl 1170.34010
Akhmet, M. U.; Turan, M.
2009
The control of boundary value problems for quasilinear impulsive integro-differential equations. Zbl 0992.93041
Akhmetov, M. U.; Zafer, A.; Sejilova, R. D.
2002
Replication of chaos. Zbl 1306.34067
Akhmet, M. U.; Fen, M. O.
2013
On the integral manifolds of the differential equation with piecewise constant argument of generalized type. Zbl 1133.34040
Akhmet, Marat
2006
An improved method for analytical modelling and anticipation of gene expression patterns. Zbl 1071.92019
Akhmet, M. U.; Öktem, Hakan; Weber, G.-W.; Gebert, J.; Pickl, S. W.
2005
Neural networks with discontinuous/impact activations. Zbl 1295.92007
Akhmet, Marat; Yılmaz, Enes
2014
The principles of $$B$$-smooth discontinuous flows. Zbl 1093.37004
Akalin, E.; Akhmet, M. U.
2005
Periodic and almost periodic solutions of systems with impulse perturbations. Zbl 0545.34030
Akhmetov, M. U.; Perestyuk, N. A.
1983
Periodic solutions of the hybrid system with small parameter. Zbl 1170.34049
Akhmet, M. U.; Büyükadalı, C.; Ergenç, T.
2008
Asymptotic equivalence of differential equations and asymptotically almost periodic solutions. Zbl 1189.34084
Akhmet, M. U.; Tleubergenova, M. A.; Zafer, A.
2007
Successive approximation method for quasilinear impulsive differential equations with control. Zbl 1125.93349
Akhmetov, M. U.; Zafer, A.
2000
The control of the boundary value problem for linear impulsive integro-differential systems. Zbl 0943.93007
Akhmetov, M.; Sejilova, R.
1999
Entrainment by chaos. Zbl 1323.34061
Akhmet, M. U.; Fen, M. O.
2014
Shunting inhibitory cellular neural networks with chaotic external inputs. Zbl 1331.92012
Akhmet, M. U.; Fen, M. O.
2013
Global exponential stability of neural networks with non-smooth and impact activations. Zbl 1258.34157
Akhmet, M. U.; Yılmaz, E.
2012
Method of Lyapunov functions for differential equations with piecewise constant delay. Zbl 1226.34070
Akhmet, M. U.; Aruğaslan, D.; Yılmaz, E.
2011
Homoclinical structure of the chaotic attractor. Zbl 1221.34124
Akhmet, M. U.
2010
On periodic solutions of differential equations with piecewise constant argument. Zbl 1165.34348
Akhmet, M. U.; Büyükadalı, C.
2008
Control and optimal response problems for quasilinear impulsive integrodifferential equations. Zbl 1259.49037
Akhmet, M. U.; Kirane, M.; Tleubergenova, M. A.; Weber, G. W.
2006
Differential properties of solutions and integral surfaces for nonlinear impulse systems. Zbl 0799.34007
Akhmetov, M. U.; Perestyuk, N. A.
1992
Replication of chaos in neural networks, economics and physics. Zbl 1319.37017
Akhmet, Marat; Fen, Mehmet Onur
2016
On periodic solutions of linear impulsive delay differential systems. Zbl 1171.34340
Akhmet, M. U.; Alzabut, J. O.; Zafer, A.
2008
Boundary value problems for higher order linear impulsive differential equations. Zbl 1099.34030
Uğur, Ö.; Akhmet, M. U.
2006
On the smoothness of solutions of impulsive autonomous systems. Zbl 1067.34006
Akhmet, M. U.
2005
Almost-periodic solutions of nonlinear impulse systems. Zbl 0693.34054
Akhmetov, M. U.; Perestyuk, N. A.
1989
Creating a chaos in a system with delay. Zbl 1263.34060
Akhmet, M. U.
2009
Controllability of the Vallée-Poussin problem for impulsive differential systems. Zbl 0941.93004
Akhmetov, M. U.; Zafer, A.
1999
The controllability of boundary-value problems for quasilinear impulsive systems. Zbl 0965.93014
Akhmetov, M. U.; Zafer, A.
1998
Differentiable dependence of the solutions of impulse systems on initial data. Zbl 0694.34003
Akhmetov, M. U.; Perestyuk, N. A.
1989
Bifurcation in autonomous and nonautonomous differential equations with discontinuities. Zbl 1390.34003
Akhmet, Marat; Kashkynbayev, Ardak
2017
Homoclinic and heteroclinic motions in economic models with exogenous shocks. Zbl 1376.91112
Akhmet, Marat; Onur Fen, Mehmet
2016
Quasilinear retarded differential equations with functional dependence on piecewise constant argument. Zbl 1285.34059
Akhmet, Marat U.
2014
Exponentially dichotomous linear systems of differential equations with piecewise constant argument. Zbl 1300.34150
Akhmet, M.
2012
Shadowing and dynamical synthesis. Zbl 1182.34009
Akhmet, M. U.
2009
Asymptotic behavior of linear impulsive integro-differential equations. Zbl 1155.45301
Akhmet, M. U.; Tleubergenova, M. A.; Yılmaz, O.
2008
Permanence of autonomous ratio-dependent predator-prey systems with piecewise constant argument of generalized type. Zbl 1165.34046
Akhmet, M. U.; Aruğaslan, D.; Liu, X.
2008
Regular and irregular discontinuous dynamics of the systemic arterial pressure. Zbl 1081.92011
Akhmet, M. U.; Bekmukhambetova, G. A.; Serinağaoğlu, Y.
2005
Control of a linear pulse systems. Zbl 0938.34059
Akhmetov, M. U.; Perestyuk, N. A.; Tleubergenova, M. A.
1995
Stability of periodic solutions of differential equations with impulse action on surfaces. Zbl 0698.34033
Akhmetov, M. U.; Perestyuk, N. A.
1989
Nonautonomous transcritical and pitchfork bifurcations in impulsive systems. Zbl 1299.34143
Akhmet, M. U.; Kashkynbayev, A.
2013
Analysis of biological integrate-and-fire oscillators. Zbl 1228.92006
Akhmet, Marat
2011
Hopfield-type neural networks systems with piecewise constant argument. Zbl 1263.34019
Akhmet, M. U.; Yilmaz, E.
2009
Bifurcation of a non-smooth planar limit cycle from a vertex. Zbl 1239.34035
Akhmet, Marat U.; Aruğaslan, Duygu
2009
Bifurcation of three-dimensional discontinuous cycles. Zbl 1239.34011
Akhmet, Marat U.; Turan, Mehmet
2009
The complex dynamics of the cardiovascular system. Zbl 1238.76078
Akhmet, M. U.
2009
Asymptotic representation of solutions of regularly perturbed systems of differential equations with nonclassical right-hand side. Zbl 0786.34004
Akhmetov, M. U.; Perestyuk, N. A.
1991
On the comparison method for differential equations with impulse action. Zbl 0712.34013
Akhmetov, M. U.; Perestyuk, N. A.
1990
Almost-periodic solutions of impulse systems. Zbl 0654.34033
Perestyuk, N. A.; Akhmetov, M. U.
1987
Almost periodic solutions of impulse systems. Zbl 0619.34045
Perestyuk, N. A.; Akhmetov, M. U.
1987
Almost periodicity, chaos, and asymptotic equivalence. Zbl 07181625
Akhmet, Marat
2020
Non-autonomous grazing phenomenon. Zbl 1384.34060
Akhmet, Marat; Kıvılcım, Ayşegül
2017
Synchronization of the cardiac pacemaker model with delayed pulse-coupling. Zbl 1300.34163
Akhmet, M.
2014
Chaotification of impulsive systems by perturbations. Zbl 1296.34108
Akhmet, Marat; Fen, Mehmet Onur
2014
Non-autonomous bifurcation in impulsive systems. Zbl 1340.34139
Akhmet, Marat; Kashkynbayev, Ardak
2013
A prototype compartmental model of blood pressure distribution. Zbl 1204.34060
Akhmet, M. U.; Bekmukhambetova, G. A.
2010
The Sturm-Liouville operator on the space of functions with discontinuity conditions. Zbl 1139.34305
Uğur, Ö.; Akhmet, M. U.
2006
Existence and stability of almost-periodic solutions of quasi-linear differential equations with deviating argument. Zbl 1082.34538
Akhmet, M. U.
2004
On asymptotic equivalence of impulsive linear homogeneous differential systems. Zbl 1132.34303
Akhmet, M. U.; Tleubergenov, M. A.
2002
On the smoothness of solutions of differential equations with a discontinuous right-hand side. Zbl 0813.34013
Akhmetov, M. U.
1993
On the expansion of solutions to differential equations with discontinuous right-hand side in a series in initial data and parameters. Zbl 0808.34011
Akhmetov, M. U.
1993
On motion with the impulse action on surfaces. Zbl 0659.34052
Akhmetov, M. U.; Perestyuk, N. A.
1988
On periodic solutions of systems with impulse action. Zbl 0539.34030
Akhmetov, M. U.; Perestyuk, N. A.
1984
Dynamics with chaos and fractals. Zbl 1439.37001
Akhmet, Marat; Fen, Mehmet Onur; Alejaily, Ejaily Milad
2020
Unpredictable solutions of linear differential and discrete equations. Zbl 1440.34041
Akhmet, Marat; Fen, Mehmet Onur; Tleubergenova, Madina; Zhamanshin, Akylbek
2019
Poincaré chaos for a hyperbolic quasilinear system. Zbl 1438.34136
Akhmet, M.; Fen, M. O.; Tleubergenova, M.; Zhamanshin, A.
2019
Generation of fractals as Duffing equation orbits. Zbl 1415.37066
Akhmet, Marat; Fen, Mehmet Onur; Alejaily, Ejaily Milad
2019
A singularly perturbed differential equation with piecewise constant argument of generalized type. Zbl 1424.34258
Akhmet, Marat; Dauylbaev, Murathan; Mirzakulova, Aziza
2018
Van der Pol oscillators generated from grazing dynamics. Zbl 1400.34050
Akhmet, M. U.; Kıvılcım, A.
2018
Almost periodicity in chaos. Zbl 1403.37032
Akhmet, Marat; Fen, Mehmet Onur
2018
Grazing in impulsive differential equations. Zbl 1390.34038
Akhmet, Marat U.; Kıvılcım, A.
2018
Stability in non-autonomous periodic systems with grazing stationary impacts. Zbl 1399.34044
Akhmet, Marat; Kivilcim, Aysegul
2017
Unpredictable points and chaos. Zbl 07249788
Akhmet, Marat; Fen, Mehmet Onur
2016
Finite-time nonautonomous bifurcation in impulsive systems. Zbl 1389.34115
Akhmet, Marat; Kashkynbayev, Ardak
2016
Analysis of impact chattering. Zbl 1399.70009
Akhmet, M.; Çağ, S.
2016
Extension of Lorenz unpredictability. Zbl 1326.34026
Akhmet, Marat; Fen, Mehmet Onur
2015
On chaotic synchronization via impulsive control and piecewise constant arguments. Zbl 1418.34107
Alwan, Mohamad S.; Liu, Xinzhi; Akhmet, Marat U.
2015
Extension of spatiotemporal chaos in glow discharge-semiconductor systems. Zbl 1361.37073
Akhmet, Marat; Rafatov, Ismail; Fen, Mehmet Onur
2014
Almost periodicity, chaos, and asymptotic equivalence. Zbl 07181625
Akhmet, Marat
2020
Dynamics with chaos and fractals. Zbl 1439.37001
Akhmet, Marat; Fen, Mehmet Onur; Alejaily, Ejaily Milad
2020
Unpredictable solutions of linear differential and discrete equations. Zbl 1440.34041
Akhmet, Marat; Fen, Mehmet Onur; Tleubergenova, Madina; Zhamanshin, Akylbek
2019
Poincaré chaos for a hyperbolic quasilinear system. Zbl 1438.34136
Akhmet, M.; Fen, M. O.; Tleubergenova, M.; Zhamanshin, A.
2019
Generation of fractals as Duffing equation orbits. Zbl 1415.37066
Akhmet, Marat; Fen, Mehmet Onur; Alejaily, Ejaily Milad
2019
A singularly perturbed differential equation with piecewise constant argument of generalized type. Zbl 1424.34258
Akhmet, Marat; Dauylbaev, Murathan; Mirzakulova, Aziza
2018
Van der Pol oscillators generated from grazing dynamics. Zbl 1400.34050
Akhmet, M. U.; Kıvılcım, A.
2018
Almost periodicity in chaos. Zbl 1403.37032
Akhmet, Marat; Fen, Mehmet Onur
2018
Grazing in impulsive differential equations. Zbl 1390.34038
Akhmet, Marat U.; Kıvılcım, A.
2018
Bifurcation in autonomous and nonautonomous differential equations with discontinuities. Zbl 1390.34003
Akhmet, Marat; Kashkynbayev, Ardak
2017
Non-autonomous grazing phenomenon. Zbl 1384.34060
Akhmet, Marat; Kıvılcım, Ayşegül
2017
Stability in non-autonomous periodic systems with grazing stationary impacts. Zbl 1399.34044
Akhmet, Marat; Kivilcim, Aysegul
2017
Replication of chaos in neural networks, economics and physics. Zbl 1319.37017
Akhmet, Marat; Fen, Mehmet Onur
2016
Homoclinic and heteroclinic motions in economic models with exogenous shocks. Zbl 1376.91112
Akhmet, Marat; Onur Fen, Mehmet
2016
Unpredictable points and chaos. Zbl 07249788
Akhmet, Marat; Fen, Mehmet Onur
2016
Finite-time nonautonomous bifurcation in impulsive systems. Zbl 1389.34115
Akhmet, Marat; Kashkynbayev, Ardak
2016
Analysis of impact chattering. Zbl 1399.70009
Akhmet, M.; Çağ, S.
2016
Extension of Lorenz unpredictability. Zbl 1326.34026
Akhmet, Marat; Fen, Mehmet Onur
2015
On chaotic synchronization via impulsive control and piecewise constant arguments. Zbl 1418.34107
Alwan, Mohamad S.; Liu, Xinzhi; Akhmet, Marat U.
2015
Neural networks with discontinuous/impact activations. Zbl 1295.92007
Akhmet, Marat; Yılmaz, Enes
2014
Entrainment by chaos. Zbl 1323.34061
Akhmet, M. U.; Fen, M. O.
2014
Quasilinear retarded differential equations with functional dependence on piecewise constant argument. Zbl 1285.34059
Akhmet, Marat U.
2014
Synchronization of the cardiac pacemaker model with delayed pulse-coupling. Zbl 1300.34163
Akhmet, M.
2014
Chaotification of impulsive systems by perturbations. Zbl 1296.34108
Akhmet, Marat; Fen, Mehmet Onur
2014
Extension of spatiotemporal chaos in glow discharge-semiconductor systems. Zbl 1361.37073
Akhmet, Marat; Rafatov, Ismail; Fen, Mehmet Onur
2014
A new method of chaos generation. Zbl 1294.34048
Akhmet, Marat; Fen, Mehmet Onur
2014
Replication of chaos. Zbl 1306.34067
Akhmet, M. U.; Fen, M. O.
2013
Shunting inhibitory cellular neural networks with chaotic external inputs. Zbl 1331.92012
Akhmet, M. U.; Fen, M. O.
2013
Nonautonomous transcritical and pitchfork bifurcations in impulsive systems. Zbl 1299.34143
Akhmet, M. U.; Kashkynbayev, A.
2013
Non-autonomous bifurcation in impulsive systems. Zbl 1340.34139
Akhmet, Marat; Kashkynbayev, Ardak
2013
Almost periodic solutions of second order neutral differential equations with functional response on piecewise constant argument. Zbl 1302.34106
Akhmet, M.
2013
Chaotic period-doubling and OGY control for the forced Duffing equation. Zbl 1253.34048
Akhmet, M. U.; Fen, M. O.
2012
Global exponential stability of neural networks with non-smooth and impact activations. Zbl 1258.34157
Akhmet, M. U.; Yılmaz, E.
2012
Exponentially dichotomous linear systems of differential equations with piecewise constant argument. Zbl 1300.34150
Akhmet, M.
2012
The period-doubling route to chaos in the relay system. Zbl 1332.37017
Akhmet, M. U.; Fen, M. O.
2012
Chaos generation in hyperbolic systems. Zbl 1444.37028
Akhmet, M. U.; Fen, M. O.
2012
Self-synchronization of the integrate-and-fire pacemaker model with continuous couplings. Zbl 1235.93029
Akhmet, M. U.
2012
Nonlinear hybrid continuous/discrete-time models. Zbl 1328.93001
Akhmet, Marat
2011
Method of Lyapunov functions for differential equations with piecewise constant delay. Zbl 1226.34070
Akhmet, M. U.; Aruğaslan, D.; Yılmaz, E.
2011
Analysis of biological integrate-and-fire oscillators. Zbl 1228.92006
Akhmet, Marat
2011
Principles of discontinuous dynamical systems. Zbl 1204.37002
Akhmet, Marat
2010
Stability in cellular neural networks with a piecewise constant argument. Zbl 1191.68484
Akhmet, M. U.; Aruğaslan, D.; Yılmaz, E.
2010
Impulsive Hopfield-type neural network system with piecewise constant argument. Zbl 1202.92001
Akhmet, M. U.; Yılmaz, E.
2010
Stability analysis of recurrent neural networks with piecewise constant argument of generalized type. Zbl 1400.34112
Akhmet, M. U.; Aruğaslan, D.; Yılmaz, E.
2010
Differential equations with state-dependent piecewise constant argument. Zbl 1195.34103
Akhmet, M. U.; Büyükadalı, C.
2010
Homoclinical structure of the chaotic attractor. Zbl 1221.34124
Akhmet, M. U.
2010
A prototype compartmental model of blood pressure distribution. Zbl 1204.34060
Akhmet, M. U.; Bekmukhambetova, G. A.
2010
Global attractivity in impulsive neural networks with piecewise constant delay. Zbl 1221.92004
Akhmet, M. U.; Yilmaz, E.
2010
Li-Yorke chaos in the system with impacts. Zbl 1153.37017
Akhmet, M. U.
2009
Devaney’s chaos of a relay system. Zbl 1221.37030
Akhmet, M. U.
2009
Lyapunov-Razumikhin method for differential equations with piecewise constant argument. Zbl 1179.34077
Akhmet, Marat; Aruğaslan, Duygu
2009
Dynamical synthesis of quasi-minimal sets. Zbl 1176.34009
Akhmet, M. U.
2009
Differential equations on variable time scales. Zbl 1170.34010
Akhmet, M. U.; Turan, M.
2009
Creating a chaos in a system with delay. Zbl 1263.34060
Akhmet, M. U.
2009
Shadowing and dynamical synthesis. Zbl 1182.34009
Akhmet, M. U.
2009
Hopfield-type neural networks systems with piecewise constant argument. Zbl 1263.34019
Akhmet, M. U.; Yilmaz, E.
2009
Bifurcation of a non-smooth planar limit cycle from a vertex. Zbl 1239.34035
Akhmet, Marat U.; Aruğaslan, Duygu
2009
Bifurcation of three-dimensional discontinuous cycles. Zbl 1239.34011
Akhmet, Marat U.; Turan, Mehmet
2009
The complex dynamics of the cardiovascular system. Zbl 1238.76078
Akhmet, M. U.
2009
Almost periodic solutions of the linear differential equation with piecewise constant argument. Zbl 1182.34093
Akhmet, M. U.
2009
Stability of differential equations with piecewise constant arguments of generalized type. Zbl 1173.34042
Akhmet, M. U.
2008
Almost periodic solutions of differential equations with piecewise constant argument of generalized type. Zbl 1166.34039
Akhmet, M. U.
2008
Asymptotic behavior of solutions of differential equations with piecewise constant arguments. Zbl 1152.34348
Akhmet, M. U.
2008
Periodic solutions of the hybrid system with small parameter. Zbl 1170.34049
Akhmet, M. U.; Büyükadalı, C.; Ergenç, T.
2008
On periodic solutions of differential equations with piecewise constant argument. Zbl 1165.34348
Akhmet, M. U.; Büyükadalı, C.
2008
On periodic solutions of linear impulsive delay differential systems. Zbl 1171.34340
Akhmet, M. U.; Alzabut, J. O.; Zafer, A.
2008
Asymptotic behavior of linear impulsive integro-differential equations. Zbl 1155.45301
Akhmet, M. U.; Tleubergenova, M. A.; Yılmaz, O.
2008
Permanence of autonomous ratio-dependent predator-prey systems with piecewise constant argument of generalized type. Zbl 1165.34046
Akhmet, M. U.; Aruğaslan, D.; Liu, X.
2008
On modeling of blood pressure distribution. Zbl 1203.76181
Akhmet, Marat; Bekmukhambetova, Gul’baram
2008
Integral manifolds of differential equations with piecewise constant argument of generalized type. Zbl 1122.34054
Akhmet, M. U.
2007
On the reduction principle for differential equations with piecewise constant argument of generalized type. Zbl 1134.34048
Akhmet, M. U.
2007
Asymptotic equivalence of differential equations and asymptotically almost periodic solutions. Zbl 1189.34084
Akhmet, M. U.; Tleubergenova, M. A.; Zafer, A.
2007
An impulsive ratio-dependent predator-prey system with diffusion. Zbl 1114.35097
Akhmet, M. U.; Beklioglu, M.; Ergenc, T.; Tkachenko, V. I.
2006
The differential equations on time scales through impulsive differential equations. Zbl 1110.34006
Akhmet, M. U.; Turan, M.
2006
Perron’s theorem for linear impulsive differential equations with distributed delay. Zbl 1101.34065
Akhmet, M. U.; Alzabut, J.; Zafer, A.
2006
On the integral manifolds of the differential equation with piecewise constant argument of generalized type. Zbl 1133.34040
Akhmet, Marat
2006
Control and optimal response problems for quasilinear impulsive integrodifferential equations. Zbl 1259.49037
Akhmet, M. U.; Kirane, M.; Tleubergenova, M. A.; Weber, G. W.
2006
Boundary value problems for higher order linear impulsive differential equations. Zbl 1099.34030
Uğur, Ö.; Akhmet, M. U.
2006
The Sturm-Liouville operator on the space of functions with discontinuity conditions. Zbl 1139.34305
Uğur, Ö.; Akhmet, M. U.
2006
Impulsive control of the population dynamics. Zbl 1133.34350
Akhmet, M. U.; Aruğaslan, D.; Beklioğlu, M.
2006
Perturbations and Hopf bifurcation of the planar discontinuous dynamical system. Zbl 1066.34008
Akhmet, M. U.
2005
An improved method for analytical modelling and anticipation of gene expression patterns. Zbl 1071.92019
Akhmet, M. U.; Öktem, Hakan; Weber, G.-W.; Gebert, J.; Pickl, S. W.
2005
The principles of $$B$$-smooth discontinuous flows. Zbl 1093.37004
Akalin, E.; Akhmet, M. U.
2005
On the smoothness of solutions of impulsive autonomous systems. Zbl 1067.34006
Akhmet, M. U.
2005
Regular and irregular discontinuous dynamics of the systemic arterial pressure. Zbl 1081.92011
Akhmet, M. U.; Bekmukhambetova, G. A.; Serinağaoğlu, Y.
2005
Existence and stability of almost-periodic solutions of quasi-linear differential equations with deviating argument. Zbl 1082.34538
Akhmet, M. U.
2004
On the general problem of stability for impulsive differential equations. Zbl 1047.34094
Akhmet, M. U.
2003
The control of boundary value problems for quasilinear impulsive integro-differential equations. Zbl 0992.93041
Akhmetov, M. U.; Zafer, A.; Sejilova, R. D.
2002
On asymptotic equivalence of impulsive linear homogeneous differential systems. Zbl 1132.34303
Akhmet, M. U.; Tleubergenov, M. A.
2002
Successive approximation method for quasilinear impulsive differential equations with control. Zbl 1125.93349
Akhmetov, M. U.; Zafer, A.
2000
Control of a boundary value problem for a linear impulsive integro-differential system. Zbl 0997.93011
Akhmetov, M. U.; Seilova, R. D.
2000
The control of the boundary value problem for linear impulsive integro-differential systems. Zbl 0943.93007
Akhmetov, M.; Sejilova, R.
1999
Controllability of the Vallée-Poussin problem for impulsive differential systems. Zbl 0941.93004
Akhmetov, M. U.; Zafer, A.
1999
The controllability of boundary-value problems for quasilinear impulsive systems. Zbl 0965.93014
Akhmetov, M. U.; Zafer, A.
1998
Control of a linear pulse systems. Zbl 0938.34059
Akhmetov, M. U.; Perestyuk, N. A.; Tleubergenova, M. A.
1995
On the smoothness of solutions of differential equations with a discontinuous right-hand side. Zbl 0813.34013
Akhmetov, M. U.
1993
On the expansion of solutions to differential equations with discontinuous right-hand side in a series in initial data and parameters. Zbl 0808.34011
Akhmetov, M. U.
1993
Periodic solutions of strongly nonlinear systems with nonclassical right- hand side in the case of a family of generating solutions. Zbl 0806.34029
Akhmetov, M. U.
1993
Periodic and almost periodic solutions of strongly nonlinear impulsive systems. Zbl 0791.34034
Akhmetov, M. U.; Perestyuk, N. A.
1992
Differential properties of solutions and integral surfaces for nonlinear impulse systems. Zbl 0799.34007
Akhmetov, M. U.; Perestyuk, N. A.
1992
...and 13 more Documents
all top 5

#### Cited by 540 Authors

 71 Akhmet, Marat Ubaydulla 13 Agarwal, Ravi P. 13 Fen, Mehmet Onur 12 Tkachenko, Victor Ivanovich 11 O’Regan, Donal 11 Pinto, Manuel 11 Wang, Jinrong 10 Alzabut, Jehad O. 10 Perestyuk, Mykola Oleksiĭovych 10 Stamov, Gani Trendafilov 10 Wang, Chao 10 Weber, Gerhard-Wilhelm 10 Zafer, Ağacık 9 Li, Chuandong 9 Liu, Zijian 9 Yılmaz, Enes 8 Assanova, Anar Turmaganbetkyzy 8 Fečkan, Michal 7 Zhong, Shou-Ming 6 Aruğaslan, Duygu 6 Kapustyan, Oleksiy V. 6 Stamova, Ivanka Milkova 6 Tokmak Fen, Fatma 5 Chiu, Kuo-Shou 5 Huang, Tingwen 5 Liu, Mingzhu 5 Liu, Xinzhi 5 Nieto Roig, Juan Jose 5 Rachůnková, Irena 5 Uğur, Ömür 5 Yaslan Karaca, Ilkay 4 Bakirova, Elmira A. 4 Dashkovskiy, Sergey N. 4 Dvornyk, A. V. 4 Feketa, Petro V. 4 Gao, Jianfang 4 Kadirbayeva, Zhazira M. 4 Li, Xiaodi 4 Luo, Albert C. J. 4 Şaylı, Mustafa 4 Teng, Zhi-dong 4 Tomeček, Jan 4 Turan, Mehmet 4 Zhou, Yong 3 Büyükadalı, C. 3 Cao, Jinde 3 Chen, Ling 3 Kropat, Erik 3 Lan, Hengyou 3 Li, Kelin 3 Li, Liping 3 Li, Yongkun 3 Liang, Hui 3 Liu, Gui Rong 3 Myslo, Yu. M. 3 Robledo, Gonzalo 3 Rodríguez-López, Rosana 3 Romaniuk, Iryna V. 3 Salman, Sanaa Moussa 3 Song, Qiankun 3 Wang, Qi 3 Wang, Qi 3 Wang, Qi 3 Xu, Daoyi 3 Yang, Dan 3 Yu, Hengguo 2 Abdeljawad, Thabet 2 Akteke-Öztürk, Basak 2 Alparslan Gök, Sırma Zeynep 2 Bai, Yuzhen 2 Belley, Jean-Marc 2 Chen, Lu 2 Chen, Wufan 2 Chen, Xiaofeng 2 Church, Kevin E. M. 2 Cui, Yi-shun 2 Dai, Chuanjun 2 Defterli, Ozlem 2 Din, Qamar 2 Donchev, Tzanko Donchev 2 Ergenç, Tanil 2 Ergören, Hilmi 2 Fan, Xiaoming 2 Ge, Weigao 2 Gong, Shuhua 2 Guo, Siyu 2 Han, Jian-qun 2 He, Zhilong 2 Huan, Songmei 2 Huang, Lihong 2 Jiang, Fuquan 2 Kartal, Senol 2 Kashkynbayev, Ardak 2 Kivilcim, Ayşegül 2 Li, An 2 Li, Bing 2 Li, Zuoan 2 Liu, He 2 Liu, Xing 2 Liu, Xiuxiang ...and 440 more Authors
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#### Cited in 115 Serials

 24 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 23 Applied Mathematics and Computation 19 Advances in Difference Equations 18 Journal of Mathematical Analysis and Applications 16 Ukrainian Mathematical Journal 13 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 13 Abstract and Applied Analysis 13 Communications in Nonlinear Science and Numerical Simulation 10 Chaos, Solitons and Fractals 10 Nonlinear Analysis. Real World Applications 10 Nonlinear Analysis. Hybrid Systems 8 Journal of Computational and Applied Mathematics 8 Nonlinear Dynamics 7 Computers & Mathematics with Applications 7 Journal of the Franklin Institute 7 Acta Applicandae Mathematicae 7 Journal of Mathematical Sciences (New York) 7 Discrete Dynamics in Nature and Society 6 Neural Networks 6 Applied Mathematical Modelling 6 Journal of Difference Equations and Applications 6 Mathematical Problems in Engineering 6 Journal of Applied Mathematics and Computing 5 Applied Mathematics Letters 5 Boundary Value Problems 4 Journal of Differential Equations 4 Acta Mathematicae Applicatae Sinica. English Series 4 Chaos 3 Mathematics and Computers in Simulation 3 Numerical Functional Analysis and Optimization 3 Applied Numerical Mathematics 3 Mathematical and Computer Modelling 3 European Journal of Operational Research 3 Computational and Applied Mathematics 3 Turkish Journal of Mathematics 3 Complexity 3 Journal of Inequalities and Applications 3 Qualitative Theory of Dynamical Systems 3 Mediterranean Journal of Mathematics 3 International Journal of Biomathematics 3 Journal of Nonlinear Science and Applications 2 Applicable Analysis 2 Journal of Applied Mathematics and Mechanics 2 Lithuanian Mathematical Journal 2 Mathematical Methods in the Applied Sciences 2 Automatica 2 Glasgow Mathematical Journal 2 Journal of Optimization Theory and Applications 2 Mathematica Slovaca 2 Optimization 2 Numerical Methods for Partial Differential Equations 2 Automation and Remote Control 2 International Journal of Computer Mathematics 2 Top 2 Bulletin des Sciences Mathématiques 2 Differential Equations and Dynamical Systems 2 Discrete and Continuous Dynamical Systems. Series B 2 Journal of Applied Mathematics 2 Communications on Pure and Applied Analysis 2 Advances in Mathematical Physics 2 Asia Pacific Journal of Mathematics 2 Applied Mathematics and Nonlinear Sciences 1 International Journal of Modern Physics B 1 Discrete Applied Mathematics 1 Indian Journal of Pure & Applied Mathematics 1 Journal of Mathematical Physics 1 Physics Letters. A 1 Fuzzy Sets and Systems 1 SIAM Journal on Control and Optimization 1 Annals of Operations Research 1 Neural Computation 1 Computational Mathematics and Mathematical Physics 1 Journal of Dynamics and Differential Equations 1 Indagationes Mathematicae. New Series 1 Journal of Nonlinear Science 1 Vestnik St. Petersburg University. Mathematics 1 Set-Valued Analysis 1 Applied Mathematics. Series B (English Edition) 1 Applicationes Mathematicae 1 Electronic Journal of Differential Equations (EJDE) 1 Journal of the Egyptian Mathematical Society 1 Fractals 1 Functional Differential Equations 1 Optimization Methods & Software 1 Geometry & Topology 1 Mathematical and Computer Modelling of Dynamical Systems 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Matematicheskie Trudy 1 Analysis (München) 1 CEJOR. Central European Journal of Operations Research 1 Journal of Dynamical and Control Systems 1 Lobachevskii Journal of Mathematics 1 International Journal of Nonlinear Sciences and Numerical Simulation 1 Journal of Nonlinear Mathematical Physics 1 Differential Equations 1 Dynamics of Continuous, Discrete & Impulsive Systems. Series B. Applications & Algorithms 1 Journal of Systems Science and Complexity 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris ...and 15 more Serials
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#### Cited in 31 Fields

 306 Ordinary differential equations (34-XX) 101 Biology and other natural sciences (92-XX) 71 Dynamical systems and ergodic theory (37-XX) 54 Systems theory; control (93-XX) 31 Partial differential equations (35-XX) 29 Numerical analysis (65-XX) 20 Operator theory (47-XX) 15 Difference and functional equations (39-XX) 14 Integral equations (45-XX) 13 Operations research, mathematical programming (90-XX) 11 Calculus of variations and optimal control; optimization (49-XX) 9 Real functions (26-XX) 8 Computer science (68-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Abstract harmonic analysis (43-XX) 5 Global analysis, analysis on manifolds (58-XX) 5 Mechanics of particles and systems (70-XX) 5 Information and communication theory, circuits (94-XX) 4 Probability theory and stochastic processes (60-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 2 General topology (54-XX) 2 Statistics (62-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Measure and integration (28-XX) 1 Special functions (33-XX) 1 Approximations and expansions (41-XX) 1 Functional analysis (46-XX) 1 Convex and discrete geometry (52-XX) 1 Fluid mechanics (76-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Statistical mechanics, structure of matter (82-XX)

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