Codimension two bifurcation in a simple delayed neuron model

He, Xing; Li, Chuandong; Huang, Tingwen; Mei, Peng

doi:10.1007/s00521-012-1181-1

Cited by 13 publications

(3 citation statements)

References 33 publications

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“…Actually, the time-delay system may have more complicated dynamics when two separate parameters or many parameters are changed simultaneously. B-T bifurcation, which is a typical codimension-2 bifurcation, is studied in [24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

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Bogdanov–Takens Bifurcation in a Shape Memory Alloy Oscillator with Delayed Feedback

Wang

2020

Complexity

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This work is focused on a shape memory alloy oscillator with delayed feedback. The main attention is to investigate the Bogdanov–Takens (B-T) bifurcation by choosing feedback parameters A 1,2 and time delay τ . The conditions for the occurrence of the B-T bifurcation are derived, and the versal unfolding of the norm forms near the B-T bifurcation point is obtained by using center manifold reduction and normal form. Moreover, it is demonstrated that the system also undergoes different codimension-1 bifurcations, such as saddle-node bifurcation, Hopf bifurcation, and saddle homoclinic bifurcation. Finally, some numerical simulations are given to verify the analytic results.

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Section: Introductionmentioning

confidence: 99%

“…□ Lemma 3 (see [24,28,29]). e bases Φ and Ψ for A and A * can be chosen such that 〈Ψ, Φ〉 � I, _ Φ � Φ 0 1 0 0 , and…”

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confidence: 99%

Bogdanov–Takens Bifurcation in a Shape Memory Alloy Oscillator with Delayed Feedback

Wang

2020

Complexity

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“…[6][7][8] Farshidianfar and Saghafi 9 studied global bifurcation behavior in spur gear systems. He et al 10 used the center manifold and normal form method to investigate codimension-two bifurcation behavior in a delayed neuron model. Tian et al 11 examined the complex nonlinear dynamics associated with smooth, discontinuous oscillators.…”

Section: Introductionmentioning

confidence: 99%

Codimension-two bifurcation analysis and chaos synchronization of a quarter-car vehicle model

Chang

2018

Advances in Mechanical Engineering

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In this study, codimension-two bifurcation analysis was used in conjunction with a novel control method to mediate chaos in a semi-active suspension system based on a quarter-car model with excitation introduced by the road surface profile. The results of bifurcation analysis indicate that the hysteretic nonlinear characteristics of the damping forces produce codimension-two bifurcation, resulting in homoclinic orbits and pitchfork bifurcation. We also characterized the complex dynamics of vehicle suspension systems using a bifurcation diagram, phase portraits, Poincaré maps, and frequency spectra. Furthermore, the largest Lyapunov exponent was used to identify the onset of chaotic motion and to verify the results of bifurcation analysis. We also developed a continuous feedback control method based on synchronization characteristics to eliminate chaotic oscillations. Finally, we conducted analysis on the robustness of parametric perturbation in suspension systems with synchronization control using Lyapunov stability theory and numerical simulations.

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Zero-Hopf singularity in bidirectional ring network model with delay

Huang

et al. 2014

Nonlinear Dyn

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Codimension two bifurcation in a simple delayed neuron model

Cited by 13 publications

References 33 publications

Bogdanov–Takens Bifurcation in a Shape Memory Alloy Oscillator with Delayed Feedback

Bogdanov–Takens Bifurcation in a Shape Memory Alloy Oscillator with Delayed Feedback

Codimension-two bifurcation analysis and chaos synchronization of a quarter-car vehicle model

Zero-Hopf singularity in bidirectional ring network model with delay

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