[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

Fractional Differential Equations

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Клініко-епідеміологічні особливості спалаху кору в м. Суми у 2014 році

Univalent functions, fractional calculus, and their applications , edited by H. M. Srivastava and S. Owa. Pp 404. £39·95. 1989. ISBN 0-7458-0701-1 (Ellis Horwood)

When possessing a potential difference between two neurons, an electromagnetic induction current appears in the Hopfield neural network (HNN), which can be emulated by a flux-controlled memristor synapse. Thus, a three-order two-neuron-based autonomous memristive HNN is presented in this paper, which is the lowest order and has not been reported in the previous studies. With the mathematical model, the detailed stability analyses for the line equilibrium are executed, so that the fold and Hopf bifurcation sets and stability region distributions in the parameter plane are obtained. Furthermore, numerical results of coexisting bifurcation patterns are investigated, which are confirmed effectively by local basins of attraction and phase plane plots. The numerical results demonstrate coexisting multi-stable patterns of the spiral chaotic patterns with different dynamic amplitudes, periodic patterns with different periodicities, and stable resting patterns with different positions in the memristive HNN. Besides, the circuit synthesis and breadboard experiments are performed to well validate the numerical simulations.

Coexisting multi-stable patterns in memristor synapse-coupled Hopfield neural network with two neurons

Fractional Order Control and Synchronization of Chaotic Systems

A robust method for new fractional hybrid chaos synchronization

In this paper, we propose three systems, namely the fractional Lozi map, the fractional Lorenz map, and the fractional flow map. We study some of the important dynamics of these maps including the bifurcation graphs. In addition, we propose control laws aimed at stabilizing and synchronizing a combination of these three maps. The convergence of the stabilized states and the synchronization errors is established by means of the linearization method. Numerical simulations are also presented to confirm the main findings of the study.

On fractional–order discrete–time systems: Chaos, stabilization and synchronization

In this paper, a new approach is proposed to investigate new type of hybrid chaos synchronization in discrete-time hyperchaotic dynamical systems. We present, based on stability theory of linear discrete-time systems and Lyapunov stability theory, a general control scheme to study the co-existence of inverse projective synchronization, inverse generalized synchronization and Q-S synchronization between arbitrary 3D hyperchaotic maps. Numerical examples and computer simulations are used to validate the theoretical results derived in this paper.

A new type of hybrid synchronization between arbitrary hyperchaotic maps

A few special chaotic systems without unstable equilibrium points have been investigated recently. It is worth noting that these special systems are different from normal chaotic ones because the classical Shilnikov criterion cannot be used to prove chaos of such systems. A novel unusual chaotic system without equilibrium is proposed in this work. We discover dynamical properties as well as the synchronization of the new system. Furthermore, a physical realization of the system without equilibrium is also implemented to illustrate its feasibility.

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Adel Ouannas

Papers

Fractional Order Control and Synchronization of Chaotic Systems

A robust method for new fractional hybrid chaos synchronization

On fractional–order discrete–time systems: Chaos, stabilization and synchronization

A new type of hybrid synchronization between arbitrary hyperchaotic maps

A Novel Chaotic System without Equilibrium