Distributed delay feedback control of a new butterfly-shaped chaotic system

Guan, Junbiao; Qin, Sen

doi:10.1016/j.ijleo.2016.03.031

Cited by 5 publications

(2 citation statements)

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“…Clearly, if Δ = 2 − 3 ⩽ 0, then the function ℎ( ) is monotone increasing in ∈ [0, ∞). Thus, when ⩾ 0 and Δ ⩽ 0, (17) has no positive real roots. On the other hand, when ⩾ 0 and Δ > 0, then…”

Section: Lemma 1 Consider the Exponential Polynomialmentioning

confidence: 99%

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Delay Feedback Control of the Lorenz-Like System

Qin

Gao

2018

Mathematical Problems in Engineering

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We choose the delay as a variable parameter and investigate the Lorentz-like system with delayed feedback by using Hopf bifurcation theory and functional differential equations. The local stability of the positive equilibrium and the existence of Hopf bifurcations are obtained. After that the direction of Hopf bifurcation and stability of periodic solutions bifurcating from equilibrium is determined by using the normal form theory and center manifold theorem. In the end, some numerical simulations are employed to validate the theoretical analysis. The results show that the purpose of controlling chaos can be achieved by adjusting appropriate feedback effect strength and delay parameters. The applied delay feedback control method in this paper is general and can be applied to other nonlinear chaotic systems.

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Section: Lemma 1 Consider the Exponential Polynomialmentioning

confidence: 99%

“…The study of [15] shows that the chaotic behavior can be stabilized on various periodic orbits by use of Pyragas timedelayed feedback control. The results of the existence of Hopf bifurcation and effectiveness of delayed feedback have been given [16][17][18][19][20][21][22][23]. Following the idea of Pyragas [12], we add a…”

Section: Introductionmentioning

confidence: 99%