Toward Analytical Chaos in Nonlinear Systems

Chapter 2Nonlinear Dynamical Systems

In this chapter, the basic theory of nonlinear dynamical systems will be introduced. Local theory, global theory, and bifurcation theory of nonlinear dynamical systems will be briefly discussed. The stability switching and bifurcation on specific eigenvectors of the linearized system at equilibrium will be discussed. The higher-order singularity and stability for nonlinear systems on the specific eigenvectors will be developed.

2.1 Continuous Systems

Definition 2.1

For , , and , consider a vector function which is ()-continuous, and there is an ordinary differential equation in a form of

2.1

where is derivative with respect to time , which is simply ...