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Dynamic analysis of the nonlinear chaotic system with multistochastic disturbances. (English) Zbl 1463.37022

Summary: The nonlinear chaotic system with multistochastic disturbances is investigated. Based on the orthogonal polynomial approximation, the method of transforming the system into an equivalent deterministic system is given. Then dynamic analysis of the nonlinear chaotic system with multistochastic disturbances can be reduced into that of its equivalent deterministic system. Especially, the Lorenz system with multistochastic disturbances is studied to demonstrate the feasibility of the given method. And its dynamic behaviors are gained including the phase portrait, the bifurcation diagram, the Poincaré section, and the maximum Lyapunov exponent.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
65C30 Numerical solutions to stochastic differential and integral equations
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
70L05 Random vibrations in mechanics of particles and systems
37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems
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