Experimental Study On Stochastic P-bifurcation Of Tri-stable VDP System With Gauss White Noise

Nonlinear problems are widely used in practical engineering applications such as physics,aerospace,biomedical,ecological environment,social science,vehicle engineering,marine structure engineering,new energy engineering,etc.In general,the internal or external disturbances always affect these systems,which are sometimes not negligible.Therefore,the effect of noise excitation on the nonlinear dynamic behavior of systems has become an important scientific problem for a long time.The noise can lead to stochastic resonance,coherence resonance,stochastic synchronization,and the essential change of the probability density distribution of the response for the steady state,which causes the stochastic P-bifurcation.So far,researchers have obtained a lot of theoretical results,but the relevant experimental research work is very little.Therefore,it is more necessary to carry out the experiment of stochastic dynamics.Compared with experiments in mechanical system,the circuit experiment is less affected by interferences and has a lot of merits such as short experimental period,lower cost,small volume,as well as convenient operation,etc.Therefore,it is an economical and practical choice to set up a circuit system to do experiments for stochastic dynamics.In order to study the stochastic dynamic behavior of a multi-stable system,we makes an experimental study on the stochastic dynamics of the generalized Van der Pol(VDP)system with the Gauss white noise.This thesis consists of four main aspects as follows.1)A stochastic dynamic experimental system of VDP with tri-stable circuit is set up.2)The effects of the supply voltage on the system responses are presented.It found that decreasing the power supply voltage can overcome the phase diagram distortion of a system response.It also shown the multi-stable bifurcation behavior of the circuit system under two kinds of power supply modes(i.e.,high voltage power supply and low voltage power supply)in experiments,and both of the two modes have tri-stable region.3)The experimental circuit is a smooth system with low voltage power supply.The stochastic P-bifurcation phenomenon induced by the Gauss white noise intensity is studied experimentally.The experimental system parameters in three cases(i.e.,three stable regions,one and two steady states)are considered and the results of the theoretical analysis are verified qualitatively.4)The experimental circuit can be treated as a non-smooth system with high voltage power supply.It established the piecewise nonlinear dynamic model of the system by considering the saturation characteristic of active elements includes operational amplifier,and analog multiplier.The stochastic dynamic experiment with Gauss white noise was conducted.The results show that a stochastic P-bifurcation actually exists in systems with noise.