Noise-Induced Hopf-Bifurcation-Type Sequence and Transition to Chaos in the Lorenz Equations

J. B. Gao, Wen-wen Tung, Nageswara Rao
2002 Physical Review Letters  
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
more » ... 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.
doi:10.1103/physrevlett.89.254101 pmid:12484887 fatcat:vpoqnmb4unhtfdbb66ubjufmeq