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Keyword

Melnikov function

Description: A function in perturbation theory that measures the separation of stable and unstable manifolds in dynamical systems and helps detect chaos.
OpenAlex ID: keywords/melnikov-function
Bifurcation of Limit Cycles by Perturbing Piecewise Hamiltonian Systems
2010 · XIA LIU, MAOAN HAN · International Journal of Bifurcation and Chaos · 183
Dynamical analysis and control of microcantilevers
1999 · M. Ashhab, M.V. Salapaka, et al. · Automatica · 180
Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles
2012 · Maoan Han, Pei Yu · Applied mathematical sciences · 152
Chaos prediction and control in MEMS resonators
2009 · Hossein S. Haghighi, Amir H.D. Markazi · Communications in Nonlinear Science and Numerical Simulation · 151
Limit Cycles Near Homoclinic and Heteroclinic Loops
2008 · Maoan Han, Junmin Yang, et al. · Journal of Dynamics and Differential Equations · 122
Morse and Melnikov functions for NLS Pde's
1994 · Y. Li, David W. McLaughlin · Communications in Mathematical Physics · 119
A theory for flow switchability in discontinuous dynamical systems
2008 · Albert C.J. Luo · Nonlinear Analysis Hybrid Systems · 117
Bifurcation of Limit Cycles from Centers and Separatrix Cycles of Planar Analytic Systems
1994 · T. R. Blows, L. M. Perko · SIAM Review · 115
Coherent atomic oscillations and resonances between coupled Bose-Einstein condensates with time-dependent trapping potential
2000 · F. Kh. Abdullaev, R. A. Kraenkel · Physical Review A · 114
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Hopf Bifurcations for Near-hamiltonian Systems
2009 · MAOAN HAN, JUNMIN YANG, et al. · International Journal of Bifurcation and Chaos · 98
A Melnikov Method for Homoclinic Orbits with Many Pulses
1998 · Roberto Camassa, Gregor Kovačič, et al. · Archive for Rational Mechanics and Analysis · 97
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Melnikov method for homoclinic bifurcation in nonlinear impact oscillators
2005 · Zhengdong Du, Weinian Zhang · Computers & Mathematics with Applications · 96
Bifurcation of limit cycles by perturbing a piecewise linear Hamiltonian system with a homoclinic loop
2012 · Feng Liang, Maoan Han, et al. · Nonlinear Analysis · 92
Generating chaos via x|x|
2001 · Kit-Sang Tang, K.F. Man, et al. · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · 91
Investigation on chaotic motion in hysteretic non-linear suspension system with multi-frequency excitations
2003 · Shaohua Li, Shaopu Yang, et al. · Mechanics Research Communications · 89
Homoclinic bifurcation and chaos control in MEMS resonators
2011 · M. Siewe Siewe, Usama H. Hegazy · Applied Mathematical Modelling · 87
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Prediction of chaos in a Josephson junction by the Melnikov-function technique
1986 · M. Bartuccelli, P. L. Christiansen, et al. · Physical review. B, Condensed matter · 84
Bifurcation theory for finitely smooth planar autonomous differential systems
2017 · Maoan Han, Lijuan Sheng, et al. · Journal of Differential Equations · 81
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On Hopf Cyclicity of Planar Systems
2000 · Maoan Han · Journal of Mathematical Analysis and Applications · 78
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Exponentially Small Splitting of Separatrices Under Fast Quasiperiodic Forcing
1997 · Amadeu Delshams, Vassili Gelfreich, et al. · Communications in Mathematical Physics · 77
Bifurcation of Limit Cycles in Piecewise Smooth Systems Via Melnikov Function
2015 · Maoan Han, Lijuan Sheng · Journal of Applied Analysis & Computation · 75
Nonsmooth homoclinic orbits, Melnikov functions and chaos in discontinuous systems
2011 · F. Battelli, M. Fečkan · Physica D Nonlinear Phenomena · 74
Limit cycle bifurcations by perturbing a cuspidal loop in a Hamiltonian system
2008 · Maoan Han, Hong Zang, et al. · Journal of Differential Equations · 72
Nonlinear Impact and Chaotic Response of Slender Rocking Objects
1991 · Solomon C. S. Yim, Huan Lin · Journal of Engineering Mechanics · 72
Asymptotic Expansions of Melnikov Functions and Limit Cycle Bifurcations
2012 · MAOAN HAN · International Journal of Bifurcation and Chaos · 68
Works count: 1,050
Citation count: 10,640
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