A New Three-Dimensional Chaotic System with Different Wing
This paper proposes a new 3D autonomous chaotic system which displays complicated dynamical behavior over a large range of parameters. This new chaotic system has five equilibrium points. Interestingly, this new system can generate two coexisting one-wing
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A New Three-Dimensional Chaotic System with Different Wing Xuanbing Yang
Abstract This paper proposes a new 3D autonomous chaotic system which displays complicated dynamical behavior over a large range of parameters. This new chaotic system has five equilibrium points. Interestingly, this new system can generate two coexisting one-wing attractors with different initial conditions. Besides, this system can generate two-wing and four-wing chaotic attractors with variation of only one parameter. Some basic dynamical behaviors of the proposed chaotic system, such as equilibrium points, bifurcation diagram and Lyapunov exponents are investigated. Keywords Chaotic system
Dynamical behavior Lyapunov exponent
9.1 Introduction Chaos is an interesting phenomenon in nonlinear dynamical systems, and has been intensively studied in the past four decades. A chaotic system is a nonlinear deterministic system that displays a complex and unpredictable behavior. The sensitive dependence on the initial conditions is a prominent characteristic of chaotic behavior. In the investigation of chaos theory and applications, it is very important to generate new chaotic systems or enhance complex dynamics and topological structure. Since Lorenz found the first chaotic attractor [1] in 1963, chaos has been intensively studied by many scholars in the last three decades [2-5]. Based on the Lorenz system, others chaotic systems were proposed in X. Yang (&) School of Information and Communication Engineering, Hunan Institute of Science and Technology, Yueyang, China e-mail: [email protected]
W. Lu et al. (eds.), Proceedings of the 2012 International Conference on Information Technology and Software Engineering, Lecture Notes in Electrical Engineering 211, DOI: 10.1007/978-3-642-34522-7_9, Ó Springer-Verlag Berlin Heidelberg 2013
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succession: Chen system [2], Lü system [3, 4], Liu system [5], etc. These chaotic systems only have three equilibrium points and two-wing chaotic attractors. Because of simple circuit implementation, it’s meaningful and challenging to constuct smooth autonomous systems with different wing attractors in both theory and engineering applications. However, there are very rare works on generating different wing chaotic attractor in a smooth system. In this paper, a novel 3D autonomous chaotic system with five equilibria is introduced. This system has been found to has many interesting complex dynamical behaviors, including chaos, period-doubling bifurcations, etc. This new system can generate two coexisting one-wing attractors with different initial conditions. Besides, this system can generate two-wing and four-wing chaotic attractors with variation of only one parameter. Therefore, it can be concluded that this chaotic system has a complicated topological structure and dynamics. Basic dynamical behaviors of the proposed chaotic system, such as equilibrium points, bifurcation diagram and Lyapunov exponents are investigated. Simulations demonstrate the brief theoretical derivations.
9.2 New 3D Chaotic
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