Abstract
Based on the construction pattern of Chen, Liu and Qi chaotic systems, a new threedimensional (3D) chaotic system is proposed by developing Lorenz chaotic system. It’s found that when parameter e varies, the Lyapunov exponent spectrum keeps invariable, and the signal amplitude can be controlled by adjusting e. Moreover, the horseshoe chaos in this system is investigated based on the topological horseshoe theory.
Highlights
In 1963, Lorenz discovered a chaotic system when studying the atmospheric convection [1]
As a basic and striking theory in chaotic dynamics, topological horseshoe with symbolic dynamics provides a powerful tool in rigorous studies of chaos in dynamical systems
Based on the topological horseshoe theory [16], we carefully pick a suitable cross-section with respect to the attractor, and find a topological horseshoe of the corresponding first-returned Poincaré map, giving a rigorous confirmation of the chaos existed in this dynamical system
Summary
In 1963, Lorenz discovered a chaotic system when studying the atmospheric convection [1]. Due to powerful applications in chemical reactions, cryptology, nonlinear circuits, secure communication and so on, researchers have paid great attention to generate new chaotic systems and analyse their dynamical behaviors and dynamical properties. Speaking, for these presented chaotic systems, the Lyapunov exponent spectrums vary gradually and rang from stable equilibrium points, periodic orbits to chaotic oscillations with the changing of system parameters. Kennedy introduced an important chaos lemma which proposed a topological horseshoe theory in continuous map [8, 9]. Based on the topological horseshoe theory [16], we carefully pick a suitable cross-section with respect to the attractor, and find a topological horseshoe of the corresponding first-returned Poincaré map, giving a rigorous confirmation of the chaos existed in this dynamical system
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