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Introduction and synchronization of a five-term chaotic system with an absolute-value term
- Introduction and synchronization of a five-term chaotic system with an absolute-value term
- Chang, Pyung Hun; Kim, Dongwon
- Issue Date
- Nonlinear Dynamics, 73(1-2), 311-323
- Article Type
- Bifurcation Diagram; Chaos; Chaos Theory; Chaotic Attractor; Chaotic Attractors; Chaotic System; Chaotic Systems; Differential Equations; Five-Term Chaotic Attractor; Frequency Spectra; Heteroclinic Orbit; Kaplan-Yorke Dimensions; Lyapunov Exponent; Lyapunov Functions; Lyapunov Methods; New Chaotic Systems; Numerical Tools
- We propose a new chaotic system that consists of only five terms, including one multiplier and one quadratic term, and one absolute-value term. It is observed that the absolute-value term results in intensifying chaoticity and complexity. The characteristics of the proposed system are investigated by theoretical and numerical tools such as equilibria, stability, Lyapunov exponents, Kaplan-Yorke dimension, frequency spectrum, Poincaré maps, and bifurcation diagrams. The existence of homoclinic and heteroclinic orbits of the proposed system is also studied by a theoretical analysis. Furthermore, synchronization of this system is achieved with a simple technique proposed by Kim et al. (Nonlinear Dyn., 2013, in press) for a practical application. © 2013 Springer Science+Business Media Dordrecht.
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