Boundary Chaos Bifurcation in a Class of Piecewise-linear Continuous Dynamical Systems
We investigate a striking boundary equilibrium bifurcation from a stable equilibrium to a chaotic in-variant set for a class of three-dimensional piecewise-linear continuous systems.Firstly,the nonexistence of homo-clinic and heteroclinic orbits is verified,which shows that the chaos phenomenon of the systems is non-Shil'nikov chaos.Further,by finding the appropriate Poincaré cross section on the switching plane,we build the second return Poincaré map through the mixed flow of two subsystems.Moreover,a computer assisted verification of chaotic invar-iant sets is presented by the topological horseshoe theory.
bifurcationasymptotically stabilitychaostopological horseshoepiecewise-linear systems
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