Constructing a new chaotic system based on the Šilnikov criterion. (English) Zbl 1053.37015

Based on the Šilnikov criterion, the authors construct a new chaotic system of quadratic polynomial ordinary differential equations in three dimensions, which has a single equilibrium point. The authors rigorously prove that this system satisfies all conditions stated in the Šilnikov theorem, which clearly reveals its chaos formation mechanism and implies the existence of Smale horseshoes. Moreover, the authors show that their simulation demonstrated there is a route to chaos through period-doubling bifurcations.


37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C28 Complex behavior and chaotic systems of ordinary differential equations
37D15 Morse-Smale systems
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