Information Entropy Of Dynamical Systems Under Random Excitation And Its Related Research

The probability distribution function is important physical quantity of the s-tochastic dynamical system.Information entropy is a function of probability dis-tribution.In many situations,distribution function is equivalent to probability distribution.The probability distribution function and information entropy evolu-tion equation are powerful tools of the stochastic dynamical system research.So,every distribution function corresponds to the only information entropy,information entropy is also a measure of the uncertainty of the system state.It can describes the disorder of any material motion(living phenomena).Information entropy time-evolution law and the effect of noise property on them have been aroused concern.According to the second law of thermodynamics,entropy flux and entropy produc-tion obtained by the heat balance equation have been studied by many scholars.Thus,we use Shannon information entropy and entropy flux,entropy production correspondence statistics to study the dynamic behaviour.Stochastic system is a system which input and output have many random fac-tors,or the system itself has some uncertainty.We often call this random force?noise or fluctuating force.This uncertainty,which is noise,it is virtually unavoidable and it plays an important role in many physical phenomena.Under certain conditions,it has a decisive effect on the systems evolution,even change the macroscopic sys-tems.At the same time,this irregular random disturb not always be a negative role,instead it plays positive effect under some conditions.Therefore,the impact of noise on the stochastic dynamical system is a meaningful issue.In practice,noise changing always be with time correlation,known as colored noise.Due to color noise more nearing to reality,it received great attention.As the "truly colored"noise,QMN's appearance arouse the attention of many researchers.So,it is worth considering the stochastic dynamical system driven by QMN.The main contents and conclusions are as follows:1.The damped harmonic oscillator driven by quasimonochromatic noise and external periodic force has been researched.We refer to the definition of Shannon's information entropy,the second law of thermodynamics and the conception of the entropy balanced equation,and obtain the upper bound of time derivative of entropy and entropy flux,entropy production.We discuss the effect of compression system parameters on the system.Get the following conclusion through analysing:The up-per bound of time derivative of entropy and entropy flux,entropy production all can reflect that the increase of parameters ? and D can promote the system transition from a non-equilibrium state relaxation to steady state.Information entropy and the relative quantities,like probability distribution functions,are efficient tools to research the stochastic dynamical system.2.We discuss a dynamical system under the effect of quasimonochromatic noise(QMN)and time-delay.By using the small delay approximation of the stochastic delay differential equations,we reduce the dimension of Fokker-Planck equation by the way of linear transformation.Based on the second law of thermodynamics and the conception of the entropy balanced equation,we obtain the exact expression for the upper bound of time derivative of entropy.The results show:The increase of parameters ? and ? can refrain the system transition from a non-equilibrium state relaxation to steady state,but the effect of parameters D is different.It can help us to understand and control the damped system more better.