The Effect Of Noise On The Dynamics Of A Discontinuous Irreversible Image

A nonlinear system usually exhibits coexistence of two or more steady states(attractors).Many of the actual systems are always in a certain noise environment,the interaction between noise and the system will have a certain impact on its dynamic behavior.The influence of noise on nonlinear dynamic system is an important way to analyze the reliability and robustness of the system.The study of its influence mechanism is beneficial to the realization of noise controlDiscontinuous systems are widespread and many discontinuous systems have coexistence of attractors.In this paper,the influences of noise on the dynamics of a discontinuous irreversible system are discussed.It has coexisted period 5 and period 6 attractors under the parameter range we are interested.The result shows that very week noise has no effect on the coexisted attractors.Under a critical noise strength,one of the two attractors is eliminated,and another attractor leaves stable.Which one of the attractor will be eliminated at this critical noise depends on the control parameter,or say the robustness at this control parameter.The previous mentioned mono-stable state changes into chaotic state when the noise strength reached a higher critical value.Therefore,the critical noise strength at which one of the coexisted attractors disappears or a mono-stable state loses it stability could be used to describe the robustness of the attractor.The numerical result shows that the robustness of the period 5 attractor decreases monotonously,but that of the period 6 attractor increases monotonously,as the increasing of the control parameter.It is due to the structural characteristics of the coexisted attractors.The critical noise strengths at which the two period attractors lose their stability divide the parameter space spanned by the noise strength and the control parameter into four regions,including those with coexisted periodic state,mono-stable period 5,mono-stable period 6 and chaotic states.With the aid of periodic control of system parameters,it's more flexible to control the state of the system,making the system state transition can occur at lower frequency and intensity.The effect of a more practical colored noise on the system dynamics is discussed.The influence of the intensity and correlation time of colored noise on the system states is studied under the specific system parameters.We find that the effect of colored noise on the discontinuous irreversible system dynamics is similar to that of Gaussian white noise control of system variables when the correlation time is small,which is expected.The required critical noise intensity of the colored noise on system variables is however greater than the Gaussian white noise on system parameters.And the critical intensity of the system increases with the increase of the correlation time.With colored noise,the range of intensity of the system being changed into another coexisting attractor is reduced or even disappears.