Quasi-Stability of Coexisting Attractors of a Neurodynamic Model with Delay

Goryunov, V. E.; Preobrazhenskaya, M. M.

doi:10.1007/s10958-022-06177-0

Cited by 1 publication

(2 citation statements)

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“…Rihan et al [26] examined the dynamics of a time-delay differential model of the tumor immune system with random noise, discussed stability and Hopf bifurcation of the deterministic system, then explored stochastic stability and the dynamics of the system in view of environmental fluctuations. Goryunov and Preobrazhenskaya [27] considered the problem of the coexistence of quasistable attractors of a neurodynamic model with delay and developed an algorithm for estimating Lyapunov exponents for the system. Yu et al [28] investigated the effectiveness of amplitude modulation in controlling bursting oscillations in a classical mechanical oscillator with time-delayed feedback, then demonstrated that an effective vibration modulation for bursting dynamics is possible if appropriate time delay and feedback gains are chosen.…”

Section: Introductionmentioning

confidence: 99%

“…[26] examined the dynamics of a time‐delay differential model of the tumor immune system with random noise, discussed stability and Hopf bifurcation of the deterministic system, then explored stochastic stability and the dynamics of the system in view of environmental fluctuations. Goryunov and Preobrazhenskaya [27] considered the problem of the coexistence of quasi‐stable attractors of a neurodynamic model with delay and developed an algorithm for estimating Lyapunov exponents for the system. Yu et al.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Orbits and chaos of a two‐fluid magnetized plasma oscillator subjected to parametric excitation with square delayed feedback

Hu,

Zhou

2023

Z Angew Math Mech

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In this manuscript, a two‐fluid magnetized plasma oscillator subjected to parametric excitation with square delayed feedback is studied both analytically and numerically. The Hamilton systems of triple‐well and narrow single‐well are discussed in detail. The scenarios of phase portraits and equilibria are given. Homoclinic and heteroclinic orbits are strictly derived. With the Melnikov method, the critical value of chaos arising from homoclinic or heteroclinic intersections is derived analytically. We have discovered some interesting dynamic phenomena, such as uncontrollable time delays with which chaos always occurs for this system. The influence of time‐delay on the chaotic property is also studied rigorously. On the basis of theoretical analysis, some numerical simulations including time histories, phase portraits, bifurcation diagrams, Poincaré sections, Lyapunov exponential spectrums and attractor basins are given. Numerical simulations are consistent with theoretical results.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%