Effects of Colored Noise on Periodic Orbits in a One-Dimensional Map

Noise can induce inverse period-doubling transition and chaos. The effects of the colored noise on periodic orbits, of the different periodic sequences in the logistic map, are investigated. It is found that the dynamical behaviors of the orbits, induced by an exponentially correlated colored noise, are different in the mergence of transition, and the effects of the noise intensity on their dynamical behaviors are different from the effects of the correlation time of noise. Remarkably, the noise can induce new periodic orbits, namely, two new orbits emerge in the period-four sequence at the bifurcation parameter value mu = 3.5, four new orbits in the period-eight sequence at mu = 3.55, and three new orbits in the period-six sequence at mu = 3.846, respectively. Moreover, the dynamical behaviors of the new orbits clearly show the resonancelike response to the colored noise.