This chapter is intended as an introduction or tutorial to nonlinear dynamical systems in one and two dimensions with an emphasis on keeping the mathematics as elementary as possible. By its nature such an approach does not have the mathematical rigor that can be found in most textbooks dealing with this topic. On the other hand it may allow readers with a less extensive background in math to d...

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.

Nonlinear dynamical systems can be uniquely investigated by a geometric theory (KCC-theory). The five KCC-invariants express intrinsic properties of the nonlinear dynamical systems. The second invariant as a curvature tensor determines the stability of the systems. The third invariant as a torsion tensor expresses the chaotic behavior. As an example, the KCC-theory is applied to a geodynamical ...

Nearly all nontrivial real-world systems are nonlinear dynamical systems. Chaos describes certain nonlinear dynamical systems that have a very sensitive dependence on initial conditions. Chaotic systems are always deterministic and may be very simple, yet they produce completely unpredictable and divergent behavior. Systems of nonlinear equations are difficult to solve analytically, and scienti...

this paper concerns the problem of robust stabilization of uncertain fractional-order non-autonomous systems. in this regard, a single input active control approach is proposed for control and stabilization of three-dimensional uncertain fractional-order systems. the robust controller is designed on the basis of fractional lyapunov stability theory. furthermore, the effects of model uncertainti...

A class of discrete dynamical systems with nonlinear feedback is considered. These systems generalize various maps arising in connection with chaotic dynamical systems, topological dynamics, and linear systems theory. We give a complete characterization of this class of systems.

In this introductory article, we survey the contents of this Theme Issue. This Theme Issue deals with a fertile region of hybrid dynamical systems that are characterized by the coexistence of continuous and discrete dynamics. It is now well known that there exist many hybrid dynamical systems with discontinuities such as impact, switching, friction and sliding. The first aim of this Issue is to...

A nonlinear dynamical model for the evolution of landslide is proposed. The parameters of this model are obtained through an improved iterative algorithm of inversion developed in the paper. Based on the nonlinear dynamical model and nonlinear dynamical systems (NDS) theory, the approaches to determining the Lyapunov exponents, the predictable timescale and the stability criterion of the evolut...

My research interests span control theory, nonlinear and robust control, robotics, hybrid systems, dynamical systems, optimization, and power systems. I develop nonlinear feedback control solutions for dynamical models ranging from robotic systems to power systems. The models of these systems are typically characterized by high dimensional state spaces, with nonlinear and hybrid dynamics. My re...