Bifurcation analysis of two disc dynamos with viscous friction and multiple time delays

Wei, Zhouchao; Zhu, Bin; Jian, Yang; Perc, Matjaž; Slavinec, Mitja

doi:10.1016/j.amc.2018.10.090

Cited by 48 publications

(23 citation statements)

References 41 publications

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“…Dynamical study of system (38) will be our future work for investigation. Moreover, it is interesting to add delay effect in system (2) to see the bifurcating behavior of resulting system [62]. On the other hand, it is also interesting to extend these results for higher dimension and to see possible hidden attractors and complex behavior for resulting system [63]- [67].…”

Section: Future Workmentioning

confidence: 99%

Dynamics and Chaos Control for a Discrete-Time Lotka-Volterra Model

Din¹,

Rafaqat

Elsadany

et al. 2020

IEEE Access

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Bifurcation theory (center manifold and Ljapunov-Schmidt reduction, normal form theory, universal unfolding, calculation of bifurcation diagrams) has become an important and very useful means in the solution of nonlinear stability problems in many branches of engineering. The present study deals with qualitative behavior of a two-dimensional discrete-time system for interaction between prey and predator. The discrete-time model has more chaotic and rich dynamical behavior as compare to its continuous counterpart. We investigate the qualitative behavior of a discrete-time Lotka-Volterra model with linear functional response for prey. The local asymptotic behavior of equilibria is discussed for discrete-time Lotka-Volterra model. Furthermore, with the help of bifurcation theory and center manifold theorem, explicit parametric conditions for directions and existence of flip and Hopf bifurcations are investigated. Moreover, two chaos control methods, that is, OGY feedback control and hybrid control strategy, are implemented. Numerical simulations are provided to illustrate theoretical discussion and their effectiveness. INDEX TERMS Lotka-Volterra model, stability, flip bifurcation, Hopf bifurcation, chaos control.

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Section: Future Workmentioning

confidence: 99%

Dynamics and Chaos Control for a Discrete-Time Lotka-Volterra Model

Din¹,

Rafaqat

Elsadany

et al. 2020

IEEE Access

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“…With the development and innovation of financial markets, scholars have found that it will be better to add time delay factor for describing the actual economic markets [27][28][29][30]. Chen [31] analyzed the complex nonlinear dynamics, such as periodicity, quasiperiodicity, and chaotic behavior in the delayed feedback of financial systems.…”

Section: Introductionmentioning

confidence: 99%

Hopf Bifurcation and Dynamic Analysis of an Improved Financial System with Two Delays

et al. 2020

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e complex chaotic dynamics and multistability of financial system are some important problems in micro-and macroeconomic fields. In this paper, we study the influence of two-delay feedback on the nonlinear dynamics behavior of financial system, considering the linear stability of equilibrium point under the condition of single delay and two delays. e system undergoes Hopf bifurcation near the equilibrium point. e stability and bifurcation directions of Hopf bifurcation are studied by using the normal form method and central manifold theory. e theoretical results are verified by numerical simulation. Furthermore, one feature of the proposed financial chaotic system is that its multistability depends extremely on the memristor initial condition and the system parameters. It is shown that the nonlinear dynamics of financial chaotic system can be significantly changed by changing the values of time delays.

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“…Many complicated and large-scale systems in nature and society can be modeled as delay differential systems, due to their flexibility and generality for representing virtually any natural and man-made structure. They have received much attention in interdisciplinary subjects including natural science [1][2][3], engineering [4], life sciences, and others [5,6]. In particular, many scientists paid their attention to the stability and bifurcation phenomena of the predator-prey system with multiple delays (see, for example, [7][8][9][10][11][12][13]).…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a diffusive delayed competition and cooperation system

Wei¹,

Zhang

2020

Open Mathematics

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In this manuscript, we first consider the diffusive competition and cooperation system subject to Neumann boundary conditions without delay terms and get the conclusion that the unique positive constant equilibrium is locally asymptotically stable. Then, we study the diffusive delayed competition and cooperation system subject to Neumann boundary conditions, and the existence of Hopf bifurcation at the positive equilibrium is obtained by regarding delay term as the parameter. By the theory of center manifold and normal form, an algorithm for determining the direction and stability of Hopf bifurcation is derived. Finally, some numerical simulations and summarizations are carried out for illustrating the theoretical analytic results.

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Bifurcation analysis of two disc dynamos with viscous friction and multiple time delays

Cited by 48 publications

References 41 publications

Dynamics and Chaos Control for a Discrete-Time Lotka-Volterra Model

Dynamics and Chaos Control for a Discrete-Time Lotka-Volterra Model

Hopf Bifurcation and Dynamic Analysis of an Improved Financial System with Two Delays

Dynamics of a diffusive delayed competition and cooperation system

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