Study On Hidden Attractors Of Two Kinds Of Nonlinear Systems

It is one of the hot issues to study the dynamic behavior of all kinds of attractors of nonlinear dynamical system.There are different types of attractors,among which the hidden attractors are the least easy to be found and sometimes ignored.Unlike Lorenz,Chen,Chua and other attractors,the hidden attractors do not contain the neighborhood of the equilibrium point,We can't use the traditional method to calculate these hidden attractors.In our production and life,the vibration phenomenon will cause unnecessary losses,among which the hidden vibration is the most difficult to be found.Therefore,the research on the hidden vibration and the hidden attractor is of great significance in the research process of complex dynamic behavior of power system.The first chapter describes the background of the study of attractor theory and the current situation of the study of hidden attractor,and introduced the main research content of the article.In the second chapter,we introduce some preliminary knowledge about hidden attractors,such as the idea of new analysis numerical algorithm,the Poincare map of harmonic linearization and the location algorithm of stable periodic solution.In the third chapter,we study the hidden attractor of a class of nonlinear Van der Pol-Duffing oscillators.Firstly,the basic characteristics of the system are discussed,and the equilibrium point is calculated.The stability of the equilibrium point is discussed according to Routh-Hurwitz criterion.Secondly,using the classical Hopf bifurcation theory of dynamical system,taking ? as the bifurcation parameter,the critical value is discussed,and the preconditions for Hopf bifurcation are obtained.Thirdly,the harmonic linearization method is used to transform the original system,and a series of continuous function sequences are introduced to iterate the system by the analysis-numerical method,and the existence of hidden attractors in the system is analyzed and verified.Finally,the hidden attractor is located by numerical simulationIn the fourth chapter,we study the hidden attractor of Rossler system.We discuss the stability of the equilibrium point of the system and obtain the preconditions for the Hopf bifurcation of the system.At the same time,we prove the existence of the hidden attractor by combining the analytical numerical method with the harmonic linearization method.Finally,we verify the rationality of the theoretical analysis by numerical simulation.The fifth chapter summarizes the hidden attractors of the two systems studied in this paper,and looks forward to the hidden attractors in the future.