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Based on the well-known topological horseshoe theorem, a new rigorous computer-assisted proof for the existence of topological horseshoe in Chen's attractor is given. An appropriate Poincare section of Chen's attractor is chosen to obtain the corresponding Poincare map which is proved to be semi-conjugate to a 2-shift map. This implies that Chen's attractor has positive topological entropy, thus in...
In this paper, a novel four-dimensional (4D) autonomous continuous time Hopfield-type neural network with two parameters is investigated. Computer simulations show that the 4D Hopfield neural network has rich and funny dynamics, and it can display equilibrium, periodic attractor, chaotic attractor and quasi-periodic attractor for different parameters. Moreover, when the system is chaotic, its positive...
The paper analyzes a new hyper-chaotic Lu attractor which has rich and complex dynamical behaviors, by utilizing Lyapunov exponent spectrum, bifurcation diagram and phase portraits. And the local bifurcation is investigated by the centre manifold theorem. With the variation of parameters, the system will undergo pitchfork bifurcation and Hopf bifurcation at zero equilibrium, respectively. Finally,...
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