Complexity Analysis of nonlinear dynamical system

Abstract

newline The research work carried out deals with the modelling and analysis of newlinenonlinear dynamical system using tools of nonlinear analysis. Modelling of newlinea nonlinear system includes a mathematical model which is a description of newlinea system using mathematical concepts and language. These models are newlinebased on the inter relations between the system variables. The relations newlinebetween the variables represent the mathematical logic or rule by which newlineinteractions in the system are taking place. Thus relationships and the model newlinecan be linear or non-linear in nature depending on the complexity of system newlineit represents. newlineThe non-linearity in the system interaction gives rise to multiple equilibrium newlinestates. The parameter values of the system decide that out of these states newlinewhich is stable and be acquired in course of its evolution with time. The newlinesteady equilibrium states of the system are determined from the stability newlineanalysis of the system. When system variables spontaneously toggle newlinebetween random states the system enters chaos. Though chaos is short term newlineit affects the system processes, variable interactions and alters parameter newlinedependence which has dire consequences on system evolution. Thus by newlinecontrolling the parameter values before factor dependence of system gets newlinealtered Chaos can be controlled and prevented. Multiple equilibrium states newlinecan occur of which some can be degenerate or non-degenerate depending on newlinethe eigen-values which are possessed by the Jacobian of the mathematical newlinesystem at the fixed points. newlinexi newlineThe stability analysis determines the stability of the equilibrium states and newlinegives the critical values of the system parameters with their inter-relations newlinefor which a particular equilibrium at particular instant of evolution becomes newlinestable or unstable. When more than one stable state of equilibrium occurs newlinefor the system at a particular value of the system parameter the system is newlinesaid to bifurcate. Through bifurcation diagrams the impact of system newlineparameters may be observed. When multiple bifurcations occurs in...