Volume 6 (2016)  

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1.  On the Synchronization of  Synaptically Coupled Nonlinear Oscillators: Theory and Experiment  Full text (PDF)

D. C. Saha, Papri Saha, Anirban Ray and A. Roychowdhury

Pages: 1-29

Abstract:  Synchronization phenomena of two nonlinear oscillator systems when coupled through a memristor are analyzed exhaustively. Due to the presence of the memristor the coupling is nonlinear and very similar to a synaptic coupler. Study of such systems are now a days extremely important due to the recent thrust on neuromorphic computing which tries to replicate the principles of operation of human brain, where a series of such systems either coupled in series or in parallel are used. Here we have considered Lorenz and Hindmarsh-Rose systems in particular. They are analyzed by numerical simulations. They are also analyzed experimentally through electronic circuits. For the experimental part, the memristor is replaced with the equivalent op-amp combination. The most striking phenomenon observed is that the synchronization shows an intermittent character with respect to parameter variations due to the existence of complex basin structure with more than one attractor. Another new aspect of this type of synchronization is its sensitive dependence on initial conditions which is due to the existence of complex basin structure with more than one attractor. As such a totally new type of synchronization is observed and explored.

2. Convergence of Nonlinear Recurrence Relations with Threshold Control and 3-Periodic Coefficients Full text (PDF)

Liping Dou and Chengmin Hou

Pages: 30-47

Abstract:  We study a difference equation as a model for a single neuron with a function satisfying the McCulloch-Pitts nonlinearity. We hope that our results will be useful in understanding interacting network models involving piecewise constant control functions.

3. Hidden Structure and Complex Dynamics of Hyperchaotic Attractors   Full text (PDF)

Safieddine Bouali                                                                                                         

Pages: 48-58

Abstract:  The paper introduces new 4-D dynamical systems ensuring full hyperchaotic patterns. Its focal statement appears in the novelty of the equation's specification of both models. Indeed, the two built systems integrating small set of nonlinear terms are not expanded variants of 3-D nonlinear systems into the fourth dimension. To explore the basic behavior of the models, we display the phase portraits of the related hyperchaotic attractors projected onto the 3-D representation spaces. The simulations exhibit hyperchaotic attractors with wings and scrolls. A collection of Poincaré Maps reveals the intricate and elegant structure of the first one. The computation of the Lyapunov exponents establishes presence of hyperchaos since two positive exponents are found. Indexes of stability of the equilibrium points corresponding to both systems are also examined. Besides, we present bifurcation diagrams highlighting the arrangement of hyperchaotic bubbles and periodic windows for a restricted range of the control parameter, for the following system. Eventually, the two systems specify dissimilar hyperchaos patterns. The phase portraits of the first model hide a very specific composition unveiled by the Poincaré maps. On the other hand, the phase portraits of the following system reveal distinct contours and uncover rich sensitivity to the control parameter.