Hyperchaos and Coexisting Attractors in a Modified van der Pol-Duffing Oscillator

被引：19

作者：

Rajagopal, Karthikeyan ^{[1
,2
,3
]}

Khalaf, Abdul Jalil M. ^{[4
]}

Wei, Zhouchao ^{[5
]}

Viet-Thanh Pham ^{[6
]}

Alsaedi, Ahmed ^{[7
]}

Hayat, Tasawar ^{[7
,8
]}

机构：

[1] Def Univ, Ctr Nonlinear Dynam, Bishoftu, Ethiopia

[2] Def Univ, Inst Res & Dev, Bishoftu, Ethiopia

[3] Mekelle Univ, Inst Energy, Mekelle, Ethiopia

[4] Minist Higher Educ & Sci Res, Baghdad, Iraq

[5] China Univ Geosci, Sch Math & Phys, Wuhan 430074, Hubei, Peoples R China

[6] Ton Due Thang Univ, Fac Elect & Elect Engn, Nonlinear Syst & Applicat, Ho Chi Minh City, Vietnam

[7] King Abdulaziz Univ, NAAM Res Grp, Jeddah, Saudi Arabia

[8] Quaid I Azam Univ, Dept Math, Islamabad 45320, Pakistan

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2019年 / 29卷 / 05期

关键词：

van der Pol-Duffing oscillator; chaos; bifurcation; multistability; FPGA; HIDDEN ATTRACTORS; CHAOTIC ATTRACTOR; EXTREME MULTISTABILITY; FPGA IMPLEMENTATION; HYPERJERK SYSTEM; DYNAMICS; SYNCHRONIZATION; REALIZATION; DESIGN; FORM;

D O I：

10.1142/S0218127419500676

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper deals with a new modified hyperchaotic van der Pol-Duffing (MVPD) snap oscillator. Various dynamical properties of the proposed system are investigated with the help of Lyapunov exponents, stability analysis of the equilibrium points and bifurcation plots. The existence of the Hopf bifurcation is established by analyzing the corresponding characteristic equation. It is also proved that the MVPD oscillator shows multistability with coexisting attractors. Various numerical simulations are conducted and presented to show the dynamical behavior of the MVPD system. To show that the system is hardware realizable, we derive the discrete model of the MVPD system using the Euler's method and using the hardware-software cosimulation, the proposed MVPD system is implemented in Field Programmable Gate Arrays. It is shown that the output of the digital implementations of the MVPD systems matches the numerical analysis.

引用

页数：17

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