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Chaotic and hyperchaotic attractors of a complex nonlinear system. (English) Zbl 1131.37036
Summary: We introduce a complex nonlinear hyperchaotic system which is a five-dimensional system of nonlinear autonomous differential equations. This system exhibits both chaotic and hyperchaotic behavior and its dynamics is very rich. Based on the Lyapunov exponents, the parameter values at which this system has chaotic, hyperchaotic attractors, periodic and quasi-periodic solutions and solutions that approach fixed points are calculated. The stability analysis of these fixed points is carried out. The fractional Lyapunov dimension of both chaotic and hyperchaotic attractors is calculated. Some figures are presented to show our results. Hyperchaos synchronization is studied analytically as well as numerically, and excellent agreement is found.

MSC:
37D45Strange attractors, chaotic dynamics
37C10Vector fields, flows, ordinary differential equations
34C28Complex behavior, chaotic systems (ODE)
34C25Periodic solutions of ODE
34C08Connections of ODE with real algebraic geometry
34D45Attractors
28A78Hausdorff and packing measures
93D15Stabilization of systems by feedback
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