Existence of periodic orbits and chaos in a class of three-dimensional piecewise linear systems with two virtual stable node-foci |
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| Affiliation: | 1. Coordinación Académica Región Altiplano Oeste, Universidad Autónoma de San Luis Potosí, Kilometro 1 carretera a Santo Domingo, 78600, Salinas de Hidalgo, San Luis Potosí, Mexico;2. División de Matemáticas Aplicadas, Instituto Potosino de Investigación Científica y Tecnológica A.C., Camino a la Presa San José 2055 col. Lomas 4a Sección, 78216, San Luis Potosí, SLP, Mexico |
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| Abstract: | In this paper, we consider a new class of piecewise linear (PWL) systems with two virtual stable node-foci (the meaning of “virtual” is from Bernardo et al. (2008)) which exhibits periodic orbits and chaos. This fact that PWL systems have no unstable equilibria but has chaos will unavoidably make the exploration of this chaos more complicated. Particular values for bifurcation diagram are provided. Based on mathematical analysis and Poincaré map, periodic orbits of this kind of system without unstable equilibrium points are derived, the corresponding existence theorems are given, and the obtained results are applied to specific examples. |
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| Keywords: | Chaos Poincaré map Piecewise linear systems Periodic orbit Virtual stable node-focus |
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