Sharif Digital Repository

One of the most surprising lessons of dynamical systems theory is that the phase spaces of simple nonlinear systems may contain strange attractors. For certain simple systems, such as pendulum, direct observations of the phase space and finding strange attractors are possible. But physical systems in which all the relevant dynamical variables can be simultaneously monitored are relatively scarce. Takens’ theory shows how a time-series of measurements of a single observable state can be often used to reconstruct qualitative features of the phase space of the system. In this research, using the time-series of one measurable state, an algorithm is proposed to control chaos. The approach... 

Chaos theory examines complex systems whose output results in large changes by applying small changes to the initial conditions. In other words, some seemingly accidental phenomena for which we have not yet found a reason can be justified with the help of chaos theory. The strong dependence of the response to the initial conditions is one of the most important features of turbulent systems, but their quasi-random behavior will be independent of these conditions after some time. Chaotic systems, as an important branch of nonlinear dynamic systems, behave close to stochastic systems. Perhaps the most important similarity between the two systems is the existence of invariant probability density...