Noise destroys the coexistence of periodic orbits of a piecewise linear map

Abstract

The effects of Gaussian white noise and Gaussian colored noise on the periodic orbits of period-5 (P-5) and period-6 (P-6) in their coexisting domain of a piecewise linear map are investigated numerically. The probability densities of some orbits are calculated. When the noise intensity is D = 0.0001, only the orbits of P-5 exist, and the coexisting phenomenon is destroyed. On the other hand, the self-correlation time τ of the colored noise also affects the coexisting phenomenon. When τc < τ < τ′c, only the orbits of P-5 appear, and the stability of the orbits of P-5 is enhanced. However, when τ > τ′c (τc and τc′ are critical values), only the orbits of P-6 exist, and the stability of the P-6 orbits is enhanced greatly. When τ < τc, the orbits of P-5 and P-6 coexist, but the stability of the P-5 orbits is enhanced and that of P-6 is weakened with τ increasing.