The targeting of chaotic trajectories uses the sensitive dependence on initial conditions to produce large (desired) changes to the trajectory using small perturbations. One important application is to directing spacecraft using very small amounts of fuel, relying on the (Hamiltonian) chaos of the three body problem consisting of the spacecraft, earth, and moon or other planet. Another applicat...

We have been motivated by a question of “anticontrol” of chaos [Schiff et al., 1994], in which recent examples [Chen & Lai, 1997] of controlling nonchaotic maps to chaos have required large perturbations. Can this be done without such brute force? In this paper, we present an example in which a family of maps, Gε, numerically displays a transverse homoclinic point, and hence a horseshoe and cha...

The hallmark of deterministic chaos, an extreme sensitivity to initial conditions, suggests that chaotic systems might be difficult if not impossible to control, since any perturbations used for control would grow exponentially in time. Indeed, this quite reasonable view was widely held until only a few years ago. Surprisingly, the basis for controlling chaos is provided by just this property, ...

Over the past two decades, researchers have been greatly interested in nonlinear dynamical systems with a special attention to those having chaotic behavior. This is due to the appearance of chaos in many scientific disciplines such as biology, chemistry, physics, mathematics and engineering applications [Skinner, 1994; Arneodo et al., 1993; Wolframm, 1985; Zhusubaliyev & Mosekilde, 2003; Lanka...

In this work, we propose a method of control and anti-control chaos based on the moving largest Lyapunov exponent using reinforcement learning. method, design reward function for learning according to exponent, which is similar average but computes corresponding recently updated time series with fixed, short length. We adopt density peaks-based clustering algorithm determine linear region diver...

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 ...