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Research Papers

Novel Hyperchaotic System and Its Circuit Implementation

[+] Author and Article Information
Chaowen Feng

College of Science,
Air Force Engineering University,
Xi'an 710051, China
e-mail: fengchaowen@163.com

Li Cai

College of Science,
Air Force Engineering University,
Xi'an 710051, China
e-mail: qianglicai@163.com

Qiang Kang

Department of Science Research,
Air Force Engineering University,
Xi'an 710051, China
e-mail: kangqiang@sina.com

Sen Wang

College of Science,
Air Force Engineering University,
Xi'an 710051, China
e-mail: wangsen@163.com

Hongmei Zhang

College of Science,
Air Force Engineering University,
Xi'an 710051, China
e-mail: phonchown@sohu.com

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received May 24, 2014; final manuscript received November 21, 2014; published online April 9, 2015. Assoc. Editor: Stefano Lenci.

J. Comput. Nonlinear Dynam 10(6), 061012 (Nov 01, 2015) (7 pages) Paper No: CND-14-1136; doi: 10.1115/1.4029227 History: Received May 24, 2014; Revised November 21, 2014; Online April 09, 2015

It is very important to generate hyperchaos with more complicated dynamics as a model for theoretical research and practical application. A new hyperchaotic system with double piecewise-linear functions in state equations is presented and physically implemented by circuit design. Based on the theoretical analyses and simulations, the hyperchaotic dynamical properties of this nonlinear system are revealed by equilibria, Lyapunov exponents, and bifurcations, verifying its unusual random nature and indicating its great potential for some relevant engineering applications such as secure communications.

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Figures

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Fig. 1

Schematic illustration of eigenspaces projected onto the (x, y, z) subspace

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Fig. 2

Stable eigenspaces and trajectory, projected onto the (x, y, w) subspace

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Fig. 3

Trajectories of system (1) with α = 6, β = 20, γ = 0.1, σ = 1.5, δ = 1, μ = 0.06. (a) x–w plane and (b) x–y–w subspace.

Grahic Jump Location
Fig. 4

Hyperchaotic attractor of system (1) for α = 6, β = 20, γ = 0.1, σ = 1.5, δ = 1, μ = 0.6. (a) x–y plane, (b) x–z plane, (c) x–w plane, (d) y–z plane, (e) y–w plane, and (f) z–w plane.

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Fig. 5

Lyapunov exponent spectrum and bifurcation diagram of system (1) with α = 6, β = 20, γ = 0.1, σ = 1.5, δ = 1, a = −3, b = 1, and μ ϵ [−2.5, 1]. (a) Lyapunov spectrum and (b) bifurcation.

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Fig. 6

Circuit realization of hyperchaotic system (1)

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Fig. 7

Phase portraits of circuit simulation results. (a) x–y plane, (b) x–z plane, (c) x–w plane, (d) y–z plane, (e) y–w plane, and (f) z–w plane.

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