Mohammad Ali Khan

Spatiotemporal synchronization of coupled Ricker maps over a complex network

In this paper, we study synchronization behaviour of coupled Ricker maps over a complex network. Our complex network is dynamic as at every update we will connect a fraction of randomly chosen sites to a node instead of their nearest neighbours. Under nearest-neighbour coupling, synchronized period 2 behaviour of the network is observed for strong coupling strength for 2 < r < 4 (where r is the parameter of the local map) but no synchronized spatiotemporal fixed point is observed. Remarkable transitions to a spatiotemporally synchronized fixed point occur with the introduction of random rewiring. With random rewiring and for low values of r, the coupled system has only a synchronized fixed point at strong coupling but it has no synchronized period 2 for weak coupling. The synchronized period 2 for weak coupling and the synchronized fixed point for strong coupling are observed for high values of r. Note that for high values of r the synchronized period-2 oscillation exists for nearest neighbour as well as random coupling. Linear stability analysis of the synchronized steady-state solution is done analytically, and from the linear stability analysis, an analytic (approximate) expression for the critical coupling coefficient bifur (at which the onset of spatiotemporal synchronization occurs) is derived. We have simulated the complete nonlinear system and observe that our prediction from theoretical analysis matches very well with the numerical results. The variation of the basin of attraction of synchronized states with respect to coupling coefficient for different random rewirings is shown. We have also investigated the variation of basin size with respect to randomness p in rewiring for various coupling coefficients. The nontrivial result of the model is the existence of order at a global level although local dynamics is chaotic.

Controlling Chaos in a Food Chain Model through Threshold Harvesting

In this paper, we propose a new harvesting strategy namely the harvesting for controlling chaotic population in a food chain model. In particular, we have taken the three species Hastings and Powell food chain model for demonstration. We have shown threshold harvesting strategy can be effectively employed to obtain a steady or cyclic behaviour from chaotic fish population by varying either the frequency of harvesting or the amount of harvesting of fish population. Numerical simulation results are presented to show the effectiveness of the scheme. We obtain steady state; limit cycle, period-2 and period-4 behaviour from chaotic Hastings and Powell model. This threshold harvesting strategy will be very useful for species conservation and fishery management

Generalized Synchronization of Nuclear Spin Generator System and the Application in Secure Communication

Abstract This paper investigates the synchronization of Nuclear spin generator system. Sufficient theorem for the synchronization of Nuclear spin generator system are deduced. A scheme of secure communication based on the synchronization of Nuclear spin generator system is presented. Numerical simulation shows its feasibility.

Generalized Lag Anti-Synchronization of Coupled Chaotic Systems

Abstract This paper aims to study the generalized lag anti-synchronization of two dynamical systems via linear transformation. The method is based on the stability criterion of linear systems and the lag anti-synchronization of driving and response systems are ensured by that all roots of characteristic equations of the jacobian matrix have negative real parts. The linear generalized lag anti-synchronization can be robustly achieved, without calculating the Lyapunov exponents. In the proposed method the functional relation between driving system and response system are also achieved.