Hopf bifurcation and hidden attractor of a modified Chua's equation

DOI10.1007/s11071-017-3777-6zbMath1380.34086OpenAlexW2753617794MaRDI QIDQ1696910

Yunxian Dai, Yiping Lin, Huitao Zhao

Publication date: 15 February 2018

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11071-017-3777-6

zbMATH Keywords

Hopf bifurcationhidden attractorattracting basinmodified Chua's equation

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Bifurcations of singular points in dynamical systems (37G10) Analytic circuit theory (94C05) Attractors of solutions to ordinary differential equations (34D45)

Related Items

Hidden attractors and multistability in a modified Chua's circuit ⋮ Coexisting Attractors, Energy Analysis and Boundary of Lü System ⋮ A Simple Nonautonomous Hidden Chaotic System with a Switchable Stable Node-Focus ⋮ Scenario of the Birth of Hidden Attractors in the Chua Circuit ⋮ DC-offset-induced hidden and asymmetric dynamics in memristive Chua's circuit

Cites Work

• Unnamed Item
• Algorithms for finding hidden oscillations in nonlinear systems. The Aizerman and Kalman conjectures and Chua's circuits
• Localization of hidden Chua's attractors
• Hopf bifurcation in an \(n\)-dimensional Goodwin model via multiple delays feedback
• The Hopf bifurcation in the Shimizu-Morioka system
• Bifurcation analysis and chaos control of the modified Chua's circuit system
• Simple chaotic flows with a line equilibrium
• Hidden attractors in dynamical systems
• Algorithm for localizing Chua attractors based on the harmonic linearization method
• Dynamical analysis of the generalized Sprott C system with only two stable equilibria
• Anti-control of Hopf bifurcation in the new chaotic system with two stable node-foci
• Robust absolute stability of Lur'e control systems in parameter space
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Determining Lyapunov exponents from a time series
• Elements of applied bifurcation theory.
• A class of initials-dependent dynamical systems
• A new chaotic attractor
• Hidden attractor in smooth Chua systems
• Dynamical behaviors of a chaotic system with no equilibria
• Elementary quadratic chaotic flows with no equilibria
• HIDDEN ATTRACTORS IN DYNAMICAL SYSTEMS. FROM HIDDEN OSCILLATIONS IN HILBERT–KOLMOGOROV, AIZERMAN, AND KALMAN PROBLEMS TO HIDDEN CHAOTIC ATTRACTOR IN CHUA CIRCUITS
• Attraktorlokalisierung des Lorenz-Systems
• YET ANOTHER CHAOTIC ATTRACTOR
• SIMPLE CHAOTIC FLOWS WITH ONE STABLE EQUILIBRIUM