Controlling Chimeras

Coupled phase oscillators model a variety of dynamical phenomena in nature and technological applications. Non-local coupling gives rise to chimera states which are characterized by a distinct part of phase-synchronized oscillators while the remaining ones move incoherently. Here, we apply the idea of control to chimera states: using gradient dynamics to exploit drift of a chimera, it will attain any desired target position. Through control, chimera states become functionally relevant; for example, the controlled position of localized synchrony may encode information and perform computations. Since functional aspects are crucial in (neuro-)biology and technology, the localized synchronization of a chimera state becomes accessible to develop novel applications. Based on gradient dynamics, our control strategy applies to any suitable observable and can be generalized to arbitrary dimensions. Thus, the applicability of chimera control goes beyond chimera states in non-locally coupled systems

Optimum PID Control of Multi-wing Attractors in A Family of Lorenz-like Chaotic Systems

Multi-wing chaotic attractors are highly complex nonlinear dynamical systems with higher number of index-2 equilibrium points. Due to the presence of several equilibrium points, randomness of the state time series for these multi-wing chaotic systems is higher than that of the conventional double wing chaotic attractors. A real coded Genetic Algorithm (GA) based global optimization framework has been presented in this paper, to design optimum PID controllers so as to control the state trajectories of three different multi-wing Lorenz like chaotic systems viz. Lu, Rucklidge and Sprott-1 system.Comment: 6 pages, 21 figures; 2012 Third International Conference on Computing, Communication and Networking Technologies (ICCCNT'12), July 2012, Coimbator

Estimation of System Parameters and Predicting the Flow Function from Time Series of Continuous Dynamical Systems

We introduce a simple method to estimate the system parameters in continuous dynamical systems from the time series. In this method, we construct a modified system by introducing some constants (controlling constants) into the given (original) system. Then the system parameters and the controlling constants are determined by solving a set of nonlinear simultaneous algebraic equations obtained from the relation connecting original and modified systems. Finally, the method is extended to find the form of the evolution equation of the system itself. The major advantage of the method is that it needs only a minimal number of time series data and is applicable to dynamical systems of any dimension. The method also works extremely well even in the presence of noise in the time series. This method is illustrated for the case of Lorenz system.Comment: 12 pages, 4 figure