Journal ArticleDOI
A Chaos Neuron Model with Fractional Differential Equation
TLDR
In this paper, a chaos neuron model represented by the fractional differential equation as a novel artificial neuron model is presented, which has an ability of a chaotic response which depends on the differential order and delay term in the dynamics.Abstract:
This paper presents a chaos neuron model represented by the fractional differential equation as a novel artificial neuron model. This model has an ability of a chaotic response which depends on the differential order and delay term in the dynamics. There is also observed a burst response in a certain parameter of chaotic region. We investigate basic characteristics of the model by some observations such as time-sequential data, bifurcation diagram for the differential order, and Lyapunov exponent analysis to the fractional differential system including delay. The result of the Lyapunov analysis confirms the existence of chaos on the presently proposed neuron model.read more
Citations
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Journal ArticleDOI
Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks
TL;DR: The present paper introduces memristor-based fractional-order neural networks and establishes the conditions on the global Mittag-Leffler stability and synchronization are established by using Lyapunov method.
Journal ArticleDOI
2012 Special Issue: Nonlinear dynamics and chaos in fractional-order neural networks
Eva Kaslik,S. Sivasundaram +1 more
TL;DR: Based on the stability analysis, the critical values of the fractional order for which Hopf bifurcations may occur are identified and Simulation results are presented to illustrate the theoretical findings and to show potential routes towards the onset of chaotic behavior when the fractions of the system increases.
Journal ArticleDOI
Non-existence of periodic solutions in fractional-order dynamical systems and a remarkable difference between integer and fractional-order derivatives of periodic functions☆
Eva Kaslik,S. Sivasundaram +1 more
TL;DR: In this paper, it was shown that the limit cycle observed in numerical simulations of a simple fractional-order neural network cannot be an exact periodic solution of the system, in contrast with integer-order derivatives.
Journal ArticleDOI
Analytic study on linear systems of fractional differential equations
TL;DR: Existence and uniqueness results are proved for two classes of linear fractional differential systems and systems of differential equations of fractional order, where the orders are equal to real number or rational numbers between zero and one.
Journal ArticleDOI
Global asymptotical ω -periodicity of a fractional-order non-autonomous neural networks
Boshan Chen,Jiejie Chen +1 more
TL;DR: This work studies global Mittag-Leffler stability and global asymptotical periodicity of the fractional-order non-autonomous neural networks, which shows that all paths of the networks, starting from arbitrary points and responding to persistent, nonconstant ω-periodic external inputs, asymPTotically converge to the same nonconstable function that may be not a solution.
References
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Journal ArticleDOI
Oscillation and Chaos in Physiological Control Systems
Michael C. Mackey,Leon Glass +1 more
TL;DR: First-order nonlinear differential-delay equations describing physiological control systems displaying a broad diversity of dynamical behavior including limit cycle oscillations, with a variety of wave forms, and apparently aperiodic or "chaotic" solutions are studied.
Book
Chaotic Neural Networks
TL;DR: In this article, a model of a single neuron with chaotic dynamics is proposed by considering the following properties of biological neurons: (1) graded responses, relative refractoriness and spatio-temporal summation of inputs.
Journal ArticleDOI
Measurement of the Lyapunov spectrum from a chaotic time series.
Masaki Sano,Yasuji Sawada +1 more
TL;DR: A new method is proposed to determine the spectrum of several Lyapunov exponents (including positive, zero, and even negative ones) from the observed time series of a single variable.
Journal ArticleDOI
Chaos in a fractional order Chua's system
TL;DR: In this article, the effects of fractional dynamics in chaotic systems were studied and it was demonstrated that systems of "order" less than three can exhibit chaos as well as other nonlinear behavior.