Nonlinear dynamical systems have been used in many disciplines to model complex behaviors, including biological motor control, robotics, perception, economics, traffic prediction, and neuroscience. While often the unexpected emergent behavior of nonlinear systems is the focus of investigations, it is of equal importance to create goal-directed behavior (e.g., stable locomotion from a system of ...

In this paper, the nonlinear dynamical systems are solved by using the homotopy analysis method (HAM).The approximation solution of this equation is calculated in the form ofa series which its components are computed easily. The existence anduniqueness of the solution and the convergence of the proposed methodare proved.The results obtained here demonstrate that the HAM is an effective and robu...

this paper considers the problem of stable limit cycles generating in a class of uncertain nonlinear systems which leads to stable oscillations in the system’s output.this is a wanted behavior in many practical engineering problems. for this purpose, first the equation of the desirable limit cycle is achieved according to shape, amplitude and frequency of the required output oscillations. then,...

We develop and test two novel computational approaches for predicting the mean linear response of a chaotic dynamical system to small change in external forcing via the fluctuation-dissipation theorem. Unlike the earlier work in developing fluctuationdissipation theorem-type computational strategies for chaotic nonlinear systems with forcing and dissipation, the new methods are based on the the...

Studies of nonlinear dynamical systems with many degrees of freedom show that the behavior of these systems is significantly different as compared with the behavior of systems with less than two degrees of freedom. These findings motivated us to carry out a survey of research focusing on the behavior of high-dimensional chaos, which include onset of chaos, routes to chaos, and the persistence o...

This paper concerns the problem of consensus tracking for multiagent systems with a dynamical leader. In particular, it proposes the corresponding explicit control laws for multiple first-order nonlinear systems, second-order nonlinear systems, and quite general nonlinear systems based on the leader-follower and the tree shaped network topologies. Several numerical simulations are given to veri...

Gene regulatory networks (GRNs) represent complex nonlinear coupled dynamical systems that models gene functions and regulations at the system level. Previous research has described GRNs as coupled nonlinear systems under parametric perturbations without considering the important aspect of stochasticity. However, a realistic model of a GRN is that of a hybrid stochastic retarded system that rep...