A Few Class Power System Dynamic Characteristic Research

Many problems in real world contain a lot of factors and the interactions between these factors maycause rich dynamics. There is little work on discrete dynamics with multiple factors and spatial dynamics.Based on the current progress of these topics, we did the following work.Firstly, we construct a dynamical model on the motion trail of intelligent mine and give the motiontrail and attack angle with respect to fire rate and time, respectively.Secondly, we construct a discrete dynamical model with individuals cannibalism and predation andinvestigate the existence and stability of positive periodic solutions. Some biological meanings are shownfor the theoretical results. Furthermore, we present a discrete dynamical systems with delay and competitionand obtain the distribution of positive periodic solutions. By structuring a curve, we separate the parametersspace into two parts Λ1and Λ2. There are at least two positive periodic solutions in domain Λ1; at least onepositive periodic solution in the curve; no positive periodic solution in domain Λ2.Thirdly, we investigate spatial dynamics with difusion and stochastic factors. We reveal the influenceof density-independent and density-dependent noise on the pattern formation and persistence of populations.By both mathematical analysis and numerical simulations, we find that density-independent noise will in-duce pattern transition from spotted pattern to stripe pattern. The number of the spotted pattern will increaseas noise intensity is small. As noise intensity increase, the number will decrease. However, when temporalcorrelation is large, stripe pattern emerges. For the spatial dynamics with density-dependent noise, noisecan induce pattern transition from spotted pattern to labyrinth pattern. What is more, noise can cause thepopulations to extinct from persistence for some values of noise intensity and temporal correlation. We alsoshow the persistence and extinction regions of populations in parameters space.Finally, we study a spatial dynamics with Allee efect and nonlinear death rate based on reactiondifusion equation. By using amplitude equations in multiple scales, we investigate the efect of interactionsbetween these two factors on the distribution of populations. The obtained results show that spatial systemswith Allee efect and nonlinear interactions can give rise to rich dynamical behaviors. As parameter δincrease, pattern structures will change from H0to Hπ. When the parameter increases to a certain value, theindividual exhibits a spiral wave pattern formation. It means that the stationary pattern is transformed intounstable state, which is bad for the persistence of populations.