Li, Jing; Lv, Zhen; Liu, Di; Xu, Yong Stochastic vibration analysis of a nonlinear oscillator with symmetric viscoelastic impact protection under wide-band noise excitations. (English) Zbl 1543.70016 Meccanica 57, No. 7, 1491-1503 (2022). MSC: 70L05 70K40 70K65 74H50 × Cite Format Result Cite Review PDF Full Text: DOI
Bongarzone, Alessandro; Guido, Margherita; Gallaire, François An amplitude equation modelling the double-crest swirling in orbital-shaken cylindrical containers. (English) Zbl 1510.76024 J. Fluid Mech. 943, Paper No. A28, 35 p. (2022). MSC: 76B07 76B45 76M45 76M22 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Elías-Zúñiga, Alex On two-scale dimension and its application for deriving a new analytical solution for the fractal Duffing’s equation. (English) Zbl 1506.70025 Fractals 30, No. 3, Article ID 2250061, 10 p. (2022). MSC: 70K40 28A80 × Cite Format Result Cite Review PDF Full Text: DOI
Dragunov, Timofeĭ Nikolaevich; Morozov, Kirill Evgen’evich; Morozov, Al’bert Dmitrievich On global dynamics in Duffing equation with quasiperiodic perturbation. (Russian. English summary) Zbl 1538.34149 Zh. Sredn. Mat. Obshch. 22, No. 2, 164-176 (2020). MSC: 34C15 34B30 34C29 34C37 34E10 70K30 70K40 × Cite Format Result Cite Review PDF Full Text: DOI MNR
Schließauf, Henrik Escaping orbits are rare in the quasi-periodic Littlewood boundedness problem. (English) Zbl 1427.37050 NoDEA, Nonlinear Differ. Equ. Appl. 26, No. 4, Paper No. 24, 21 p. (2019). Reviewer: Piotr Garbaczewski (Opole) MSC: 37J46 37J40 70K43 70K40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Jiang, Tao; Yang, Zhiyan; Jing, Zhujun Bifurcations and chaos in the Duffing equation with parametric excitation and single external forcing. (English) Zbl 1377.34047 Int. J. Bifurcation Chaos Appl. Sci. Eng. 27, No. 8, Article ID 1750125, 31 p. (2017). MSC: 34C15 70K40 34C37 34C29 34C28 70K28 34C23 34D10 × Cite Format Result Cite Review PDF Full Text: DOI
Johannessen, Kim The Duffing oscillator with damping. (English) Zbl 1332.70025 Eur. J. Phys. 36, No. 6, Article ID 065020, 13 p. (2015). MSC: 70K40 × Cite Format Result Cite Review PDF Full Text: DOI
Högele, Michael; Pavlyukevich, Ilya Metastability in a class of hyperbolic dynamical systems perturbed by heavy-tailed Lévy type noise. (English) Zbl 1316.60095 Stoch. Dyn. 15, No. 3, Article ID 1550019, 26 p. (2015). MSC: 60H10 60G51 60G52 37A20 60J60 60J75 × Cite Format Result Cite Review PDF Full Text: DOI
Stefanescu, Ion Sabba The onset of bifurcations in the forced Duffing equation with damping. (English) Zbl 1270.34094 Int. J. Bifurcation Chaos Appl. Sci. Eng. 23, No. 2, Article ID 1330006, 64 p. (2013). MSC: 34C25 34C15 34C23 37E10 × Cite Format Result Cite Review PDF Full Text: DOI
Pakdemirli, Mehmet; Karahan, M. M. Fatih Multiple scales Lindstedt Poincaré method for strongly nonlinear forced oscillations. (English) Zbl 1230.65080 J. Appl. Funct. Anal. 6, No. 3, 258-265 (2011). MSC: 65L05 34A34 34C10 70K40 × Cite Format Result Cite Review PDF
Wang, Qiudong; Ott, William Dissipative homoclinic loops of two-dimensional maps and strange attractors with one direction of instability. (English) Zbl 1229.37029 Commun. Pure Appl. Math. 64, No. 11, 1439-1496 (2011). MSC: 37D45 37C10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Du, Juan; Cui, Minggen Solving the forced Duffing equation with integral boundary conditions in the reproducing kernel space. (English) Zbl 1213.65106 Int. J. Comput. Math. 87, No. 9, 2088-2100 (2010). Reviewer: Johannes Schropp (Konstanz) MSC: 65L10 34B15 34K28 42B05 46C05 47B32 × Cite Format Result Cite Review PDF Full Text: DOI
Akgün, D.; Çankaya, İ.; Peyton Jones, J. C. A symbolic algorithm for the automatic computation of multitone-input harmonic balance equations for nonlinear systems. (English) Zbl 1170.70002 Nonlinear Dyn. 56, No. 1-2, 179-191 (2009). MSC: 70-08 70K40 68W30 × Cite Format Result Cite Review PDF Full Text: DOI
Darvishi, M. T.; Karami, A.; Shin, Byeong-Chun Application of He’s parameter-expansion method for oscillators with smooth odd nonlinearities. (English) Zbl 1223.70065 Phys. Lett., A 372, No. 33, 5381-5384 (2008). MSC: 70K40 74B20 34A34 34C60 × Cite Format Result Cite Review PDF Full Text: DOI
Girgin, Zekeriya Combining differential quadrature method with simulation technique to solve nonlinear differential equations. (English) Zbl 1195.70005 Int. J. Numer. Methods Eng. 75, No. 6, 722-734 (2008). MSC: 70-08 70K25 70K40 × Cite Format Result Cite Review PDF Full Text: DOI
Piao, Daxiong; Xin, Na The pseudo almost periodic solution of the forced pendulum equation. (Chinese. English summary) Zbl 1174.34410 Period. Ocean Univ. China 37, No. 4, 573-575 (2007). MSC: 34C27 34C15 × Cite Format Result Cite Review PDF
Ganji, D. D.; Tari, Hafez; Kalantari, R.; Shahiri, M. Approximate explicit solutions of homotopy perturbation and perturbation methods for forced nonlinear oscillation of quasi-harmonic system. (English) Zbl 1293.34049 Far East J. Dyn. Syst. 9, No. 2, 165-174 (2007). MSC: 34C10 34D15 × Cite Format Result Cite Review PDF
Gandzha, Ivan S.; Lukomsky, Vasyl P. Uniform expansions of periodic solutions for the third superharmonic resonance. (English) Zbl 1081.70011 Nonlinear Dyn. 37, No. 3, 171-179 (2004). MSC: 70K30 70K42 70K40 × Cite Format Result Cite Review PDF Full Text: DOI
Dixit, Purnima; Saha, L. M. On sensitivity to initial conditions and chaos. (English) Zbl 1079.37502 J. Math. Sci. (N.S.), Delhi 2, 1-9 (2003). MSC: 37D45 82C03 37N05 × Cite Format Result Cite Review PDF
Blekhman, I. I.; Landa, P. S. Conjugate resonances in nonlinear systems under biharmonic impact. Vibro-induced bifurcations. (Russian) Zbl 1084.70513 Izv. Vyssh. Uchebn. Zaved., Prikl. Nelinejn. Din. 10, No. 1-2, 44-51 (2002). Reviewer: Andrei Zemskov (Moskva) MSC: 70K30 70K50 70K40 37N05 × Cite Format Result Cite Review PDF
He, Xiaoling; Stallybrass, Michael Drop induced impact response of a printed wiring board. (English) Zbl 1032.74603 Int. J. Solids Struct. 39, No. 24, 5979-5990 (2002). MSC: 74M20 70K40 × Cite Format Result Cite Review PDF Full Text: DOI
Tchoukuegno, R.; Nana Nbendjo, B. R.; Woafo, P. Resonant oscillations and fractal basin boundaries of a particle in a \(\phi ^6\) potential. (English) Zbl 1010.70017 Physica A 304, No. 3-4, 362-378 (2002). MSC: 70K55 70K44 37N05 37D45 × Cite Format Result Cite Review PDF Full Text: DOI
Shi, Jinlin Forced almost periodic oscillation of second order nonlinear equation. (English) Zbl 1017.34050 Math. Sci. Res. Hot-Line 5, No. 8, 49-59 (2001). Reviewer: Klaus R.Schneider (Berlin) MSC: 34C27 × Cite Format Result Cite Review PDF
Nichols, J. M.; Virgin, L. N. Practical evaluation of invariant measures for the chaotic response of a two-frequency excited mechanical oscillator. (English) Zbl 1004.70020 Nonlinear Dyn. 26, No. 1, 67-86 (2001). MSC: 70K55 70K40 37N05 × Cite Format Result Cite Review PDF Full Text: DOI
Zúñiga, A. E.; Beatty, M. F. Forced vibrations of a body supported by viscohyperelastic shear mountings. (English) Zbl 1040.74027 J. Eng. Math. 40, No. 4, 333-353 (2001). Reviewer: Irina Alexandrovna Bolgrabskaya (Donetsk) MSC: 74H45 74H55 74B20 × Cite Format Result Cite Review PDF Full Text: DOI
Xu, Yuxiu; Bao, Wenbo; Schiehlen, W.; Hu, Haiyan A 1/3 pure subharmonic solution and transient process for the Duffing’s equation. (English) Zbl 1008.70014 Appl. Math. Mech., Engl. Ed. 22, No. 5, 586-592 (2001). MSC: 70K40 × Cite Format Result Cite Review PDF Full Text: DOI
Nikitina, N. V. Regular and irregular motions in Duffing oscillator. (English. Russian original) Zbl 1002.70018 Int. Appl. Mech. 36, No. 1, 128-133 (2000); translation from Prikl. Mekh., Kiev 36, No. 1, 139-144 (2000). Reviewer: E. Ya. Smirnov (St.Peterburg) MSC: 70K40 × Cite Format Result Cite Review PDF
Virgin, Lawrence N. Introduction to experimental nonlinear dynamics. A case study in mechanical vibration. (English) Zbl 0966.70001 Cambridge: Cambridge University Press. xvi, 256 p. (2000). Reviewer: Yuri N.Sankin (Ul’yanovsk) MSC: 70-01 70-05 70K40 70K55 70K50 × Cite Format Result Cite Review PDF
Mira, C.; Touzani-Qriouet, M.; Kawakami, H. Bifurcation structures generated by the nonautonomous Duffing equation. (English) Zbl 0970.34031 Int. J. Bifurcation Chaos Appl. Sci. Eng. 9, No. 7, 1363-1379 (1999). Reviewer: Abdelkader Boucherif (Dhahran) MSC: 34C23 70K50 70K40 37G99 × Cite Format Result Cite Review PDF Full Text: DOI
Cao, Qingjie; Zhang, Tiande; Li, Jiuping A study of the static and global bifurcations for Duffing equation. (English) Zbl 0991.70018 Appl. Math. Mech., Engl. Ed. 20, No. 12, 1413-1420 (1999). Reviewer: I.Gumowski (Thoiry) MSC: 70K50 70K40 74H60 × Cite Format Result Cite Review PDF Full Text: DOI
Szemplińska-Stupnicka, W.; Tyrkiel, E. Sequences of global bifurcations and multiple chaotic transients in a mechanical driven oscillator. (English) Zbl 0964.70020 Moon, Francis C. (ed.), IUTAM symposium on new applications of nonlinear and chaotic dynamics in mechanics. Proceedings of the IUTAM symposium held in Ithaca, NY, USA, July 27-August 1, 1997. Dordrecht: Kluwer Academic Publishers. Solid Mech. Appl. 63, 81-91 (1999). Reviewer: William J.Satzer jun.(St.Paul) MSC: 70K55 70K50 70K40 × Cite Format Result Cite Review PDF
von Wagner, Utz On the calculation of the probability density of stochastically excited nonlinear oscillators by orthogonal functions. (German) Zbl 0947.70544 ZAMM, Z. Angew. Math. Mech. 79, Suppl. 2, S323-S324 (1999). MSC: 70L05 70K40 70-08 × Cite Format Result Cite Review PDF
Wang, Zaihong Multiplicity of periodic solutions of semilinear Duffing’s equation at resonance. (English) Zbl 0977.34036 J. Math. Anal. Appl. 237, No. 1, 166-187 (1999). Reviewer: Anna Capietto (MR 2000i:34081) MSC: 34C25 37E40 34B15 × Cite Format Result Cite Review PDF Full Text: DOI
Padovan, Joe; Sawicki, Jerzy T. Nonlinear vibrations of fractionally damped systems. (English) Zbl 0929.70017 Nonlinear Dyn. 16, No. 4, 321-336 (1998). MSC: 70K40 70K60 × Cite Format Result Cite Review PDF Full Text: DOI
Tang, Chun-Lei Solvability of the forced Duffing equation at resonance. (English) Zbl 0915.34032 J. Math. Anal. Appl. 219, No. 1, 110-124 (1998). Reviewer: B.Cheshankov (Sofia) MSC: 34C25 × Cite Format Result Cite Review PDF Full Text: DOI
Fyrillas, M. M.; Szeri, A. J. Control of ultra- and subharmonic resonances. (English) Zbl 0894.34057 J. Nonlinear Sci. 8, No. 2, 131-159 (1998). MSC: 34H05 34C15 34D45 × Cite Format Result Cite Review PDF Full Text: DOI
Denman, Harry H. Approximate invariants and Lagrangians for autonomous, weakly nonlinear systems. II: Linear friction. (English) Zbl 0891.70012 Int. J. Non-Linear Mech. 33, No. 2, 301-314 (1998). MSC: 70K40 × Cite Format Result Cite Review PDF Full Text: DOI
Wang, Chengwen Generalized upper and lower solution method for the forced Duffing equation. (English) Zbl 0866.34037 Proc. Am. Math. Soc. 125, No. 2, 397-406 (1997). Reviewer: K.R.Schneider (Berlin) MSC: 34C25 34B15 34C15 × Cite Format Result Cite Review PDF Full Text: DOI
Komatsu, Yukie; Kano, Tadayoshi; Matsumura, Akitaka A bifurcation phenomenon for the periodic solutions of the Duffing equation. (English) Zbl 0955.34026 J. Math. Kyoto Univ. 37, No. 2, 191-209 (1997). Reviewer: C.Mira (Quint) MSC: 34C23 37G15 34C25 × Cite Format Result Cite Review PDF Full Text: DOI
Belyakova, G. V.; Belyakov, L. A. On bifurcations of periodic orbits in the van der Pol-Duffing equation. (English) Zbl 0887.34035 Int. J. Bifurcation Chaos Appl. Sci. Eng. 7, No. 2, 459-462 (1997). MSC: 34C23 37G99 34C25 70K40 × Cite Format Result Cite Review PDF Full Text: DOI
Janicki, K. L.; Szemplińska-Stupnicka, W. Subharmonic resonances in a driven oscillator: Bifurcation structures and transitions to chaos. (English) Zbl 0903.70019 Eur. J. Mech., A 16, No. 4, 671-694 (1997). Reviewer: I.Grosu (Iaşi) MSC: 70K50 70K40 37D45 × Cite Format Result Cite Review PDF
Yuan, Rong Existence of almost periodic solutions of Duffing equations. (Chinese. English summary) Zbl 0866.34038 J. Beijing Norm. Univ., Nat. Sci. 32, No. 3, 296-301 (1996). MSC: 34C27 × Cite Format Result Cite Review PDF
Bar-Yoseph, P. Z.; Fisher, D.; Gottlieb, O. Spectral element methods for nonlinear temporal dynamical systems. (English) Zbl 0884.70003 Comput. Mech. 18, No. 4, 302-313 (1996). Reviewer: F.Zhang (Singapore) MSC: 70-08 70K40 65L20 65L60 × Cite Format Result Cite Review PDF Full Text: DOI
Van Dooren, R.; Janssen, H. A continuation algorithm for discovering new chaotic motions in forced Duffing systems. (English) Zbl 0854.65057 J. Comput. Appl. Math. 66, No. 1-2, 527-541 (1996). Reviewer: T.E.Simos (Xanthi) MSC: 65L05 34A34 34C23 37D45 70K40 65L06 × Cite Format Result Cite Review PDF Full Text: DOI
Bar-Yoseph, P. Z.; Fisher, D.; Gottlieb, O. Spectral element methods for nonlinear spatio-temporal dynamics of an Euler-Bernoulli beam. (English) Zbl 0895.73076 Comput. Mech. 19, No. 2, 136-151 (1996). MSC: 74S30 74K10 × Cite Format Result Cite Review PDF Full Text: DOI
Pielorz, A. Dynamic analysis of a nonlinear discrete-continuous torsional system by means of wave method. (English) Zbl 0899.70016 Z. Angew. Math. Mech. 75, No. 9, 691-698 (1995). Reviewer: Liu Yanzhu (Shanghai) MSC: 70K40 74H45 × Cite Format Result Cite Review PDF Full Text: DOI
Berger, M. S.; Zhang, Luping New method for large quasiperiodic nonlinear oscillations with fixed frequencies for the nondissipative second type Duffing equation. (English) Zbl 0944.34037 Topol. Methods Nonlinear Anal. 6, No. 2, 283-293 (1995). Reviewer: Patricio L.Felmer (MR 97d:34043) MSC: 34C27 35J60 35J20 × Cite Format Result Cite Review PDF Full Text: DOI
Luo, Albert C. J. Criterion of stochastic layer near a planar homoclinic orbit of nonlinear dynamical system. (English) Zbl 0898.70017 J. Hydrodyn., Ser. B 7, No. 2, 35-50 (1995). Reviewer: Á.Bosznay (Budapest) MSC: 70L05 70K40 70K50 × Cite Format Result Cite Review PDF
Cvetićanin, L. An approximate method for obtaining self-excited vibration of the rotor. (English) Zbl 0873.70015 Teor. Primen. Meh. 20, 53-58 (1994). Reviewer: T.Atanackovic (Novi Sad) MSC: 70K40 74H45 × Cite Format Result Cite Review PDF
Berger, M. S.; Zhang, Luping A new method for large quasiperiodic nonlinear oscillations with fixed frequencies for the nondissipative forced Duffing equation. I. (English) Zbl 0847.34051 Panam. Math. J. 4, No. 2, 1-21 (1994). MSC: 34C27 70K40 × Cite Format Result Cite Review PDF
Roy, R. Valéry Noise perturbations of a nonlinear system with multiple steady states. (English) Zbl 0824.70016 Int. J. Non-Linear Mech. 29, No. 5, 755-773 (1994). Reviewer: M.D.Lax (Long Beach) MSC: 70L05 70K40 × Cite Format Result Cite Review PDF Full Text: DOI
Denman, Harry H. Approximate invariants and Lagrangians for autonomous, weakly nonlinear systems. (English) Zbl 0809.70017 Int. J. Non-Linear Mech. 29, No. 3, 409-419 (1994). MSC: 70K40 70H03 × Cite Format Result Cite Review PDF Full Text: DOI
Angenent, Sigurd A variational interpretation of Melnikov’s function and exponentionally small separatrix splitting. (English) Zbl 0810.34037 Salamon, Dietmar (ed.), Symplectic geometry. Based on lectures given at a workshop and conference held at the University of Warwick, GB in August 1990. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 192, 5-35 (1993). Reviewer: Th.J.Bartsch (Heidelberg) MSC: 34C37 34C29 58E05 37G99 × Cite Format Result Cite Review PDF
Infeld, E.; Lenkowska, T.; Thompson, J. M. T. Erosion of the basin of stability of a floating body as caused by dam breaking. (English) Zbl 0796.76010 Phys. Fluids, A 5, No. 10, 2315-2316 (1993). MSC: 76B15 76B25 76E30 × Cite Format Result Cite Review PDF Full Text: DOI
Ding, Tongren; Iannacci, Rita; Zanolin, Fabio Existence and multiplicity results for periodic solutions of semilinear Duffing equations. (English) Zbl 0785.34033 J. Differ. Equations 105, No. 2, 364-409 (1993). Reviewer: P.Smith (Keele) MSC: 34C25 34B30 × Cite Format Result Cite Review PDF Full Text: DOI
Qian, Dingbian; You, Jiangong Periodic solutions of forced second order equations with oscillatory time map. (English) Zbl 0782.34049 Differ. Integral Equ. 6, No. 4, 793-806 (1993). Reviewer: Ding Tongren (Beijing) MSC: 34C25 × Cite Format Result Cite Review PDF
Gupta, Chaitan P. Solvability of a forced autonomous Duffing’s equation with periodic boundary conditions in the presence of damping. (English) Zbl 0785.34024 Appl. Math., Praha 38, No. 3, 195-203 (1993). Reviewer: C.D.Chirila (Iaşi) MSC: 34B15 47J05 34C25 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Ding, Tongren; Zanolin, Fabio Subharmonic solutions of second order nonlinear equations: A time-map approach. (English) Zbl 0778.34027 Nonlinear Anal., Theory Methods Appl. 20, No. 5, 509-532 (1993). Reviewer: H.-J.Bangen (Immenstaad) MSC: 34C25 70K40 × Cite Format Result Cite Review PDF Full Text: DOI
Morozov, A. D. On the global behavior of self-oscillatory systems. (English) Zbl 0873.34025 Int. J. Bifurcation Chaos Appl. Sci. Eng. 3, No. 1, 195-200 (1993). MSC: 34C23 70K40 37J99 × Cite Format Result Cite Review PDF Full Text: DOI
Davies, Huw G.; Liu, Qiang The response spectrum of a nonlinear oscillator. (English) Zbl 0757.70018 J. Appl. Mech. 59, No. 2, pt. 1, 459-462 (1992). MSC: 70L05 70K40 × Cite Format Result Cite Review PDF Full Text: DOI
Dmitriev, A. S.; Komlev, U. A.; Turaev, D. V. Bifurcation phenomena in the 1:1 resonant Horn for the forced van der Pol - Duffing equation. (English) Zbl 0878.34032 Int. J. Bifurcation Chaos Appl. Sci. Eng. 2, No. 1, 93-100 (1992). MSC: 34C23 37D45 70K40 34C37 × Cite Format Result Cite Review PDF Full Text: DOI
Stewart, H. B.; Thompson, J. M. T.; Lansbury, A. N.; Ueda, Y. Generic patterns of bifurcation governing escape from potential wells. (English) Zbl 0760.34034 Int. J. Bifurcation Chaos Appl. Sci. Eng. 1, No. 1, 265-267 (1991). Reviewer: C.Mira (Toulouse) MSC: 34C23 × Cite Format Result Cite Review PDF Full Text: DOI
Lamnabhi-Lagarrigue, F.; Leroux, P.; Viennot, X. G. Combinatorial approximations of Volterra series by bilinear systems. (English) Zbl 0789.34005 Bonnard, Bernard (ed.) et al., Analysis of controlled dynamical systems. Proceedings of a conference held in Lyon, France, July 1990. Boston, MA: Birkhäuser. Prog. Syst. Control Theory. 8, 304-315 (1991). Reviewer: E.Thandapani (Salem) MSC: 34A25 × Cite Format Result Cite Review PDF
Beatty, Millard F.; Bhattacharyya, Ranjan Stability of the free vibrational motion of a vehicular body supported by rubber shear mountings with quadratic response. (English) Zbl 0738.73039 Int. J. Non-Linear Mech. 24, No. 5, 401-414 (1989). MSC: 74H45 70K20 70K25 × Cite Format Result Cite Review PDF Full Text: DOI
Mrziglod, Thomas Analytische und numerische Untersuchungen zu verzweigenden Oszillationen bei nichtlinearen Schwingungssystemen. (Analytical and numerical investigations of bifurcating oscillations in nonlinear vibrational systems). (German) Zbl 0715.70024 Köln: Univ., Math.-Naturwiss. Fak., Diss. 119 S. (1989). Reviewer: Á.Bosznay MSC: 70K40 37G99 65L07 × Cite Format Result Cite Review PDF
Bhattacharyya, Ranjan Stability of the forced vibrational motion of a vehicular body supported by rubber shear mountings with quadratic response. (English) Zbl 0713.70023 Int. J. Non-Linear Mech. 24, No. 6, 467-482 (1989). MSC: 70K40 74H45 × Cite Format Result Cite Review PDF Full Text: DOI
Nieto, Juan J.; Sanchez, Luis Periodic boundary value problem for some Duffing equations. (English) Zbl 0723.34019 Differ. Integral Equ. 1, No. 4, 399-408 (1988). MSC: 34B15 34C25 × Cite Format Result Cite Review PDF
Fazekas, F. Chaotic behaviour caused by bifurcations at nonlinear dynamical systems. II. (English) Zbl 0695.34035 Bull. Appl. Math. 51, No. 587, 29-46 (1988). Reviewer: P.Polacik MSC: 34C15 70K40 × Cite Format Result Cite Review PDF
Ueda, Yoshisuke; Nakajima, Hiroyuki; Hikihara, Takashi; Stewart, H. Bruce Forced two-well potential Duffing’s oscillator. (English) Zbl 0684.58026 Dynamical systems approaches to nonlinear problems in systems and circuits, Proc. Conf. Qual. Methods Anal. Nonlinear Dyn., Henniker/UK 1986, 128-137 (1988). Reviewer: W.Sarlet MSC: 37D45 34C15 × Cite Format Result Cite Review PDF
Drábek, Pavel A resonance problem for nonlinear Duffing equation. (English) Zbl 0646.34051 Commentat. Math. Univ. Carol. 29, No. 2, 205-215 (1988). MSC: 34C25 34B15 34C15 × Cite Format Result Cite Review PDF Full Text: EuDML
Holmes, Philip Knots and orbit genealogies in nonlinear oscillators. (English) Zbl 0646.34041 New directions in dynamical systems, London Math. Soc. Lect. Note Ser. 127, 150-191 (1988). Reviewer: P.Holmes MSC: 34C15 57M25 34C25 × Cite Format Result Cite Review PDF
Broer, H. W. Quasi-periodic Hopf-bifurcations in forced oscillations. (English) Zbl 0668.34040 Proc. 15th Braz. Colloq. Math. Poǫs de Caldas/Braz. 1985, 317-328 (1987). Reviewer: J.H.Tian MSC: 34C25 34C15 × Cite Format Result Cite Review PDF
Invernizzi, Sergio On the periodic BVP for the forced Duffing equation. (English) Zbl 0651.34066 Rend. Ist. Mat. Univ. Trieste 19, No. 1, 64-75 (1987). Reviewer: P.N.Bajaj MSC: 34K99 34B15 34C25 × Cite Format Result Cite Review PDF
Xu, Zhenyuan; Liu, Zengrong Some phenomena for weak spring Duffing equation in subharmonic and ultrasubharmonic region. (English) Zbl 0647.70030 Appl. Math. Mech., Engl. Ed. 8, 427-431 (1987). MSC: 70K30 70K40 35B35 × Cite Format Result Cite Review PDF Full Text: DOI
Forbes, Lawrence K. Periodic solutions of high accuracy to the forced Duffing equation: Perturbation series in the forcing amplitude. (English) Zbl 0637.34020 J. Aust. Math. Soc., Ser. B 29, No. 1-2, 21-38 (1987). Reviewer: O.Akinyele MSC: 34B30 34C25 × Cite Format Result Cite Review PDF Full Text: DOI
Wiggins, Stephen; Holmes, Philip Homoclinic orbits in slowly varying oscillators. (English) Zbl 0622.34041 SIAM J. Math. Anal. 18, 612-629 (1987). Reviewer: Charles A.Swanson (Vancouver) MSC: 34C25 34D10 37J99 37G99 70H05 34A12 × Cite Format Result Cite Review PDF Full Text: DOI Link
Byatt-Smith, J. G. 2\(\pi\) periodic solutions of Duffing’s equation with negative stiffness. (English) Zbl 0615.34038 SIAM J. Appl. Math. 47, 60-91 (1987). Reviewer: P.Drábek MSC: 34C25 34E10 × Cite Format Result Cite Review PDF Full Text: DOI
Schmidt, G. Globales Verhalten erzwungener nichtlinearer Schwingungen und Einsetzen von Chaos. (Global behaviour of forced nonlinear oscillations and onset of chaos). (German) Zbl 0612.70027 Z. Angew. Math. Mech. 67, 17-22 (1987). MSC: 70K30 70-08 37-XX × Cite Format Result Cite Review PDF Full Text: DOI
Miletta, Peter D. Qualitative behavior of solutions to an averaged Duffing equation. (English) Zbl 0641.70018 Q. Appl. Math. 44, 141-154 (1986). Reviewer: G.Schweitzer MSC: 70K30 37-XX × Cite Format Result Cite Review PDF
Byatt-Smith, J. G. Regular and chaotic solutions of Duffing’s equation for large forcing. (English) Zbl 0628.34049 IMA J. Appl. Math. 37, 113-145 (1986). Reviewer: F.Brauer MSC: 34C28 × Cite Format Result Cite Review PDF Full Text: DOI
Smith, Russell A. Some applications of Hausdorff dimension inequalities for ordinary differential equations. (English) Zbl 0622.34040 Proc. R. Soc. Edinb., Sect. A 104, 235-259 (1986). Reviewer: H.Hochstadt MSC: 34C25 34C15 28D99 × Cite Format Result Cite Review PDF Full Text: DOI
Semenova, N. N. Homoclinic solutions of Duffing’s equation. (English. Russian original) Zbl 0597.70023 Vestn. Leningr. Univ., Math. 19, No. 1, 77-84 (1986); translation from Vestn. Leningr. Univ., Ser. I 1986, No. 1, 63-70 (1986). MSC: 70K40 34C25 37-XX 70-08 × Cite Format Result Cite Review PDF
Dowell, E. H.; Pezeshki, C. On the understanding of chaos in Duffing’s equation including a comparison with experiment. (English) Zbl 0592.73053 J. Appl. Mech. 53, 5-9 (1986). MSC: 74G60 37D45 × Cite Format Result Cite Review PDF Full Text: DOI
Akulenko, L. D. Forced periodic motions of a quasiperiodic system with a lag. (English. Russian original) Zbl 0575.70023 J. Appl. Math. Mech. 48(1985), 459-465 (1984); translation from Prikl. Mat. Mekh. 48, 647-656 (1984). MSC: 70K40 × Cite Format Result Cite Review PDF Full Text: DOI
Seifert, George On the number of periodic solutions of some 2-dimensional periodic systems. (English) Zbl 0573.34032 Differential and integral equations, Proc. 12th Midwest Conf., Iowa City/Iowa 1983, 101-106 (1985). MSC: 34C25 × Cite Format Result Cite Review PDF
Bellman, R.; Bentsman, J.; Meerkov, S. M. On vibrational stabilizability of nonlinear systems. (English) Zbl 0548.93063 J. Optimization Theory Appl. 46, 421-430 (1985). MSC: 93D15 70K20 93C10 34C15 34A34 70K40 × Cite Format Result Cite Review PDF Full Text: DOI
Bollen, J. A. M. Synchronization theory for forced oscillations in second-order systems. (English) Zbl 0544.93035 J. Optimization Theory Appl. 45, 545-576 (1985). MSC: 93C15 34C15 34C25 93C10 34E10 70K40 × Cite Format Result Cite Review PDF Full Text: DOI
Thompson, J. M. T. An introduction to nonlinear dynamics. (English) Zbl 0565.70024 Appl. Math. Modelling 8, 157-168 (1984). Reviewer: P.C.Rath MSC: 70K05 70K40 × Cite Format Result Cite Review PDF Full Text: DOI
Wood, David Rational-Fourier-series approximations for periodic boundary-value problems. (English) Zbl 0562.65051 IMA J. Appl. Math. 33, 229-244 (1984). Reviewer: D.A.Sánchez MSC: 65L05 65L60 34C25 34A34 42A10 × Cite Format Result Cite Review PDF Full Text: DOI
Kojima, H.; Saito, H. Forced vibrations of a beam with a nonlinear dynamic vibration absorber. (English) Zbl 0547.73041 J. Sound Vib. 88, 559-568 (1983). MSC: 74H45 74K10 × Cite Format Result Cite Review PDF Full Text: DOI
Nakajima, Fumio; Seifert, George The number of periodic solutions of 2-dimensional periodic systems. (English) Zbl 0476.34033 J. Differ. Equations 49, 430-440 (1983). MSC: 34C25 × Cite Format Result Cite Review PDF Full Text: DOI
Birman, V.; Elisakoff, I.; Singer, J. On the effect of axial compression on the bounds of simple harmonic motion. (English) Zbl 0533.70020 Isr. J. Technol. 20, 254-258 (1982). Reviewer: G.Dittrich MSC: 70K30 70K40 70K99 34A34 × Cite Format Result Cite Review PDF
Nocilla, Silvio On integration of Duffing’s equation and its generalizations. (Italian) Zbl 0532.70019 Atti Accad. Sci. Torino, Cl. Sci. Fis. Mat. Nat. 115, Suppl., 81-97 (1982). Reviewer: H.J.Bangen MSC: 70K30 70K40 × Cite Format Result Cite Review PDF
Borisenko, V. G.; Gulyaev, V. I.; Dekhtyaryuk, E. S. Nonlinear oscillations of mechanical systems. (English. Russian original) Zbl 0504.70019 Sov. Appl. Mech. 17, 932-937 (1982); translation from Prikl. Mekh. 17, No. 10, 93-99 (1981). Reviewer: Leslie Month (Berkeley) MSC: 70K20 34C25 34D10 37G99 37J40 × Cite Format Result Cite Review PDF Full Text: DOI
Holmes, Philip J. Averaging and chaotic motions in forced oscillations. (English) Zbl 0472.70024 SIAM J. Appl. Math. 38, 65-80 (1980). MSC: 70K20 37D45 34C25 70K99 70L05 × Cite Format Result Cite Review PDF Full Text: DOI
Nguyen Van Dao Nonlinear oscillations of third order systems. II. Non-autonomous systems. (English) Zbl 0465.34024 J. Tech. Phys. 21, 125-134 (1980). MSC: 34C15 70K30 34D20 × Cite Format Result Cite Review PDF
Engin, H.; Ablowitz, M. J.; Askar, A.; Cakmak, A. S. Resonant non-linear vibrations of continuous systems. II. Damped and transient behavior. (English) Zbl 0459.73017 Int. J. Non-Linear Mech. 14, 235-246 (1979). MSC: 74H45 74J20 74L10 35L05 35Q99 × Cite Format Result Cite Review PDF Full Text: DOI
Finizio, Norman J. Harmonic solutions of Duffing’s equation forced by periodic impulses. (English) Zbl 0407.70014 Bul. Inst. Politeh. Iași, Secț. I 23(27), No. 3-4, 53-60 (1977). MSC: 70J99 × Cite Format Result Cite Review PDF