Analysis of a new coupled hyperchaotic model and its topological types

Ming, Hao; Hu, Hanping; Zheng, Jun

doi:10.1007/s11071-021-06692-w

Cited by 13 publications

(2 citation statements)

References 44 publications

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“…The approach of deriving the existence of chaos via Marotto's theorem has been employed in a lot of literature such as [31,35], where, however, some details of proving snapback repellers are omitted. For example, in Section 5 of [35], the repelling neighborhood of the fixed point z 0 is obtained via numerical simulations and the relation f 3 (z 1 ) = z 0 is verified via numerical calculations.…”

Section: Snapback Repellers and Chaosmentioning

confidence: 99%

Stability and chaos of the duopoly model of Kopel: A study based on symbolic computations

Kongyan

Wei

et al. 2023

Preprint

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Since Kopel's duopoly model was proposed about three decades ago, there are almost no analytical results on the equilibria and their stability in the asymmetric case. The first objective of our study is to fill this gap. This paper analyzes the asymmetric duopoly model of Kopel analytically by using several tools based on symbolic computations. We discuss the possibility of the existence of multiple positive equilibria and establish necessary and sufficient conditions for a given number of positive equilibria to exist. The possible positions of the equilibria in Kopel's model are also explored. Furthermore, in the asymmetric model of Kopel, if the duopolists adopt the best response reactions or homogeneous adaptive expectations, we establish rigorous conditions for the local stability of equilibria for the first time. The occurrence of chaos in Kopel's model seems to be supported by observations through numerical simulations, which, however, is challenging to prove rigorously. The second objective is to prove the existence of snapback repellers in Kopel's map, which implies the existence of chaos in the sense of Li–Yorke according to Marotto's theorem.

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Section: Snapback Repellers and Chaosmentioning

confidence: 99%

Stability and chaos of the duopoly model of Kopel: A study based on symbolic computations

Kongyan

Wei

et al. 2023

Preprint

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“…In this work, we propose a new 4-D hyperchaotic four-wing system by adding a feedback control to the Li chaotic system [10]. Bifurcation analysis helps to understand the novel features of new chaotic and hyperchaotic systems [11][12][13]. We carry out a detailed bifurcation analysis of the new 4-D hyperchaotic four-wing system and describe the changes in the qualitative properties of the new hyperchaotic four-wing system by varying the parameter values.…”

Section: Introductionmentioning

confidence: 99%

A new 4-D hyperchaotic four-wing system, its bifurcation analysis, complete synchronization and circuit simulation

2023

Archives of Control Sciences

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In this work, we modify the dynamics of 3-D four-wing Li chaotic system (Li et al. 2015) by introducing a feedback controller and obtain a new 4-D hyperchaotic four-wing system with complex properties. We show that the new hyperchaotic four-wing system have three saddle-foci balance points, which are unstable. We carry out a detailed bifurcation analysis for the new hyperchaotic four-wing system and show that the hyperchaotic four-wing system has multistability and coexisting attractors. Using integral sliding mode control, we derive new results for the master-slave synchronization of hyperchaotic four-wing systems. Finally, we design an electronic circuit using MultiSim for real implementation of the new hyperchaotic four-wing system.

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Stability and Chaos of the Duopoly Model of Kopel: A Study Based on Symbolic Computations

Li,

Chen,

Niu

et al. 2024

Comput Econ

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Analysis of a new coupled hyperchaotic model and its topological types

Cited by 13 publications

References 44 publications

Stability and chaos of the duopoly model of Kopel: A study based on symbolic computations

Stability and chaos of the duopoly model of Kopel: A study based on symbolic computations

A new 4-D hyperchaotic four-wing system, its bifurcation analysis, complete synchronization and circuit simulation

Stability and Chaos of the Duopoly Model of Kopel: A Study Based on Symbolic Computations

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