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Noise-induced Hopf-bifurcation-type sequence and transition to chaos in the lorenz equations
J B Gao1, Wen-Wen Tung, Nageswara Rao
1Department of Electrical and Computer Engineering, EB 559, University of Florida, Gainesville 32611, USA.
Abstract:
We study the effects of noise on the Lorenz equations in the parameter regime admitting two stable fixed point solutions and a strange attractor. We show that noise annihilates the two stable fixed point attractors and evicts a Hopf-bifurcation-like sequence and transition to chaos. The noise-induced oscillatory motions have very well defined period and amplitude, and this phenomenon is similar to stochastic resonance, but without a weak periodic forcing. When the noise level exceeds certain threshold value but is not too strong, the noise-induced signals enable an objective computation of the largest positive Lyapunov exponent, which characterize the signals to be truly chaotic.