Homoclinic and heteroclinic orbits in a modified Lorenz system. (English) Zbl 1057.37019

Summary: This paper presents a mathematically rigorous proof for the existence of chaos in a modified Lorenz system using the theory of Shil’nikov bifurcations of homoclinic and heteroclinic orbits. Together with its dynamical behavior, which has been extensively studied, the chaotic dynamics of the modified Lorenz system are now much better understood, providing a rigorous theoretic foundation to support studies and applications of this important class of chaotic systems.


37C29 Homoclinic and heteroclinic orbits for dynamical systems
34C37 Homoclinic and heteroclinic solutions to ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
Full Text: DOI


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