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Based on mathematical analysis, this paper provides a methodology to ensure the existence of homoclinic orbits in a class of three-dimensional piecewise affine systems. In addition, two chaotic generators are provided to illustrate the effectiveness of the method. [ABSTRACT FROM AUTHOR]

To confirm the numerically demonstrated chaotic behavior in a chaotic system with only one stable equilibrium reported by Wang and Chen, we resort to Poincaré map technique and present a rigorous computer-assisted verification of horseshoe chaos by virtue of topological horseshoes theory. [ABSTRACT FROM AUTHOR]

This paper studies the hyperchaotic dynamics in a four-dimensional Hopfield neural network by virtue of topological horseshoe. Two different horseshoes (chaotic invariant sets) are found in this network with the same parameters. Numerical studies show that the first one expands only one-dimensionally and the second one expands two-dimensionally. Computer simulation also shows that there exists a heteroclinic connection from the second horseshoe to the first one, which indicates that the chaotic set of this system can have a very complicated structure composed of different kinds of expansions. [ABSTRACT FROM AUTHOR]

This paper presents some rigorous arguments on a chaotic strange attractor in a spacecraft power system, which is a 3D system with hysteresis switching. By carefully picking a suitable cross-section with respect to the attractor, we find a topological horseshoe of the corresponding third-returned Poincaré map, thus giving a rigorous verification of the existence of chaos in this system. Numerical computation shows that the two Lyapunov exponents of the Poincaré map are both positive and that there exists a two-directional expansion in this horseshoe, suggesting that this attractor is hyperchaotic in nature. [ABSTRACT FROM AUTHOR]

We obtain numerically a horseshoe in a Poincaré map derived from a cellular neural network described by four-dimensional autonomous ordinary differential equations. Contrary to the horseshoe numerically found in the Hodgkin–Huxley model, which showed evidence that the Poincaré map derived from the Hodgkin–Huxley model has just one expanding direction on some invariant subset, the horseshoe obtained in this paper proves that the Poincaré map derived from the neural network have two expanding directions on some invariant subset. [ABSTRACT FROM AUTHOR]

In this paper, it is shown that chaos can take place in simple three-dimensional cellular neural networks with connection matrices satisfying Dale's rule. In addition, a rigorous computer-assisted verification of chaoticity in these cellular neural networks is given by virtue of topological horseshoe theory. [ABSTRACT FROM AUTHOR]

In this paper, we demonstrate chaos in low dimensional cellular neural networks for some weight matrices. To verify chaoticity of the dynamics in these cellular neural networks, we consider a cross-section properly chosen for the attractors obtained and study the dynamics of the corresponding Poincaré maps, and rigorously verify the existence of horseshoe in the manner of computer-assisted proof arguments. [ABSTRACT FROM AUTHOR]

In this paper we revisit the well-known Chua's circuit and give a discussion on entropy of this circuit. We present a formula for the topological entropy of a Chua's circuit in terms of the Poincaré map derived from the ordinary differential equations of this Chua's circuit by computer simulation arguments. [ABSTRACT FROM AUTHOR]

This letter reports the finding of a chaotic attractor in a very simple three-dimensional autonomous hybrid system, which is obtained by applying a discontinuous feedback to a stable linear system. This attractor is different from the known chaotic attractors investigated in the literature and is globally attractive. [ABSTRACT FROM AUTHOR]