The waveform-relaxation method is an iterative method for analysis of nonlinear dynamical system. Two waveform-relaxation algorithms i.e., Gauss-Seidel(GS) and Gauss-Jacobi(GJ) algorithms are presented for analysis of dynamical system. Then organization of a waveform-relaxation circuit simulator is described.

This paper treats a nonlinear dynamical system with both continuous-time and discrete-time variables as a differential–difference–algebraic equation (DDA) or a hybrid dynamical system, presents a fundamental analyzing method of such a DDA system for local sampling, asymptotical stability, singular perturbations and bifurcations, and further shows that there exist four types of generic codimensi...

We consider the nonlinear dynamic system x Δ t atgyt, y Δ t −ft, x σ t. We establish some necessary and sufficient conditions for the existence of oscillatory and nonoscillatory solutions with special asymptotic properties for the system. We generalize the known results in the literature. Some examples are included to illustrate the results.

This paper analyzes the current use of artificial states in modeling practice and proposes a new form of equations for the purpose of modeling dynamic systems. These balance dynamics equations are used to formulate dynamic processes that help to find the solution of nonlinear systems of equations.

Readily veri"able conditions under which a dynamical system of the form x "f (x) possesses an unbounded solution are presented. The results are illustrated by showing they can be used to infer results about lack of global stabilizability for nonlinear control systems. The key observation in the paper is that behaviour at in"nity can be studied using local methods applied to an auxiliary system....

Presented in this paper are readily veriiable conditions under which a dynamical system of the form _ x = f(x) possesses an unbounded solution. This result is illustrated by showing it can be used to infer results about lack of global stabilizability for nonlinear control systems. The key observation in the paper is that behaviour at innnity can be studied using local methods applied to an auxi...

In this paper, we address the problem of designing nonlinear observers for dynamical discretetime systems with both constant and time-varying delay nonlinearities. The nonlinear system is assumed to verify the usual Lipschitz condition that permits us to transform the nonlinear system into a linear time-delay system with structured uncertainties. The existence of the observer-gain is ensured by...

This paper is concerned with the study of fuzzy dynamical systems. Let (XM ) be a fuzzy metric space in the sense of George and Veeramani. A fuzzy discrete dynamical system is given by any fuzzy continuous self-map dened on X. We introduce the various fuzzy shad- owing and fuzzy topological transitivity on a fuzzy discrete dynamical systems. Some relations between this notions have been proved.