‎in the following text for arbitrary $x$ with at least two elements‎, ‎nonempty countable set $gamma$‎ ‎we make a comparative study on the collection of generalized shift dynamical systems like $(x^gamma,sigma_varphi)$ where $varphi:gammatogamma$ is an arbitrary self-map‎. ‎we pay attention to sub-systems and combinations of generalized shifts with counterexamples regarding devaney‎, ‎exact dev...

For the time-delay feedback control of chaos synchronization problem, an idea of Lyapunov functional with time-delay decomposition is presented. Some delay-dependent synchronization criteria are formulated in the form of matrix inequalities. The controller gain with maximum allowed timedelay can be achieved by solving a set of linear matrix inequalities (LMIs). A simulation example is given to ...

The complicated behaviours seen in chaotic dynamical systems can be tamed in extremely subtle ways. The application of miniscule bounded parameter perturbations can transform chaos into order, provided those perturbations are appropriately chosen. Many methods have been derived to control chaotic behaviour in a wide range of systems. Moreover, they often require no knowledge of the underlying d...

This paper studies the problem of controlling chaos in Lorenz system. By dividing Lorenz system into two subsystems, the small gain theorem is used to design linear feedback controllers to make the equilibrium points of the controlled system globally asymptotically stable. Thus chaos in Lorenz system disappears under the controller.

It has been pointed out that a chaos control technique wherein a weak excitation is added to the system could be useful for the control of friction at the nanoscale. We examine the claim that this technique can achieve chaos control even though the added excitation is weak. We show that this claim is only valid for the particular case of systems with very shallow potential wells. However, the a...

Analyses and investigations on river flow behavior are major issues in design, operation and studies related to water engineering. Thus, recently the application of chaos theory and new techniques, such as chaos theory, has been considered in hydrology and water resources due to relevant innovations and ability. This paper compares the performance of chaos theory with Anfis model and discusses ...