**
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.

**
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