Abstract
The existence of heteoclinic loop which connects the saddle focus equilibrium points is analyzed for a three-dimensional differential system based on heteoclinic orbit Shilnikov method, which proves the system possesses "horseshoe" chaos. Then the system bifurcation, Lyapunov exponent, Poincare mapping are studied by numerical analysis. In addition, adaptive backstepping design is used to control this system with three unknown key parameters, and an algorithm of this controller is presented. Finally, we make some numerical simulations of the system in order to verify the analytic results.
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