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Zero-Hopf bifurcation and Hopf bifurcation for smooth Chua’s system [PDF]
Advances in Difference Equations, 2018 Based on the fact that Chua’s system is a classic model system of electronic circuits, we first present modified Chua’s system with a smooth nonlinearity, described by a cubic polynomial in this paper. Then, we explore the distribution of the equilibrium
Junze Li, Yebei Liu, Zhouchao Wei
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The cusp–Hopf bifurcation [PDF]
International Journal of Bifurcation and Chaos, 2007 The coalescence of a Hopf bifurcation with a codimension-two cusp bifurcation of equilibrium points yields a codimension-three bifurcation with rich dynamic behavior.
W F Langford, J Harlim
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Optimization of Hopf bifurcation points
SIAM Journal on Scientific Computing, 2023 We introduce a numerical technique for controlling the location and stability properties of Hopf bifurcations in dynamical systems. The algorithm consists of solving an optimization problem constrained by an extended system of nonlinear partial ...
Rognes, Marie +6 more
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Asymptotic analysis of subcritical Hopf–homoclinic bifurcation
Physica D: Nonlinear Phenomena, 2000 This paper discusses the mathematical analysis of a codimension two bifurcation determined by the coincidence of a subcritical Hopf bifurcation with a homoclinic orbit of the Hopf equilibrium.
Allan R Willms
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Influence of Coil Current and Oil Film Thickness on Hopf Bifurcation of MLDSB
Energies, 2022 Magnetic-liquid double-suspension bearing (MLDSB) is composed of an electromagnetic supporting system and a hydrostatic supporting system. Due to its greater supporting capacity and stiffness, it is appropriate for middle-speed applications, overloading,
Jianhua Zhao +6 more
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Bogdanov–Takens bifurcation of a Holling IV prey–predator model with constant-effort harvesting
Journal of Inequalities and Applications, 2021 A prey–predator model with constant-effort harvesting on the prey and predators is investigated in this paper. First, we discuss the number and type of the equilibria by analyzing the equations of equilibria and the distribution of eigenvalues.
Lifang Cheng, Litao Zhang
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Hopf Bifurcation, Hopf-Hopf Bifurcation, and Period-Doubling Bifurcation in a Four-Species Food Web [PDF]
Mathematical Problems in Engineering, 2018 Complex dynamics of a four-species food web with two preys, one middle predator, and one top predator are investigated. Via the method of Jacobian matrix, the stability of coexisting equilibrium for all populations is determined. Based on this equilibrium, three bifurcations, i.e., Hopf bifurcation, Hopf-Hopf bifurcation, and period-doubling ...
Huayong Zhang +5 more
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Advances in Difference Equations, 2020 In this paper, stochastic Hopf–Hopf bifurcation of the discrete coupling logistic system with symbiotic interaction is investigated. Firstly, orthogonal polynomial approximation of discrete random function in the Hilbert spaces is applied to reduce the ...
Maosong Yang, Shaojuan Ma
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Cluster Oscillation of a Fractional-Order Duffing System with Slow Variable Parameter Excitation
Fractal and Fractional, 2022 The complicated dynamic behavior of a fractional-order Duffing system with slow variable parameter excitation is investigated. The stability and bifurcation behavior of the fast subsystem are analyzed by using the dynamic theory of fractional-order ...
Xianghong Li, Yanli Wang, Yongjun Shen
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Energy Science & Engineering, 2023 The strong coupling, multivariate, and nonlinear characteristics of the mathematical model of a doubly‐fed induction generator (DFIG) make it challenging to analyze the bifurcation category of the DFIG. Therefore, in this study, we developed a method for
Wei Chen +4 more
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