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Analysis of a new quadratic 3D chaotic attractor. (English) Zbl 1383.34065

Summary: A new three-dimensional chaotic system is introduced. Basic properties of this system show that its corresponding attractor is topologically different from some well-known systems. Next, detailed information on dynamic of this system is obtained numerically by means of Lyapunov exponents spectrum, bifurcation diagrams, and 0-1 chaos indicator test. We finally prove existence of this chaotic attractor theoretically using Shil’nikov theorem and undetermined coefficient method.

MSC:

34C28 Complex behavior and chaotic systems of ordinary differential equations
34D45 Attractors of solutions to ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34H10 Chaos control for problems involving ordinary differential equations
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