Global $$O(t^{-\alpha })$$ Synchronization of Fractional-Order Non-autonomous Neural Network Model with Time Delays Through Centralized Data-Sampling Approach

In this paper, fractional-order recurrent neural network models with Caputo Derivative are investigated. Firstly, we mainly focus our attention on Hopf bifurcation conditions for commensurate fractional-order network with time delay to reveal the essence that fractional-order equation can simulate the activity of neuron oscillation. Secondly, for incommensurate fractional-order neural network model, we prove the stability of the zero equilibrium point to show that incommensurate fractional-order neural network still converges to zero point. Finally, Hopf bifurcation conditions for the incommensurate fractional-order neural network model are first obtained using bifurcation theory based on commensurate fractional-order system.

Download Full-text

Centralized Data-Sampling Approach for GlobalOt-αSynchronization of Fractional-Order Neural Networks with Time Delays

Discrete Dynamics in Nature and Society ◽

10.1155/2017/6157292 ◽

2017 ◽

Vol 2017 ◽

pp. 1-10 ◽

Cited By ~ 1

Author(s):

Jin-E Zhang

Keyword(s):

Neural Networks ◽

Fractional Order ◽

Time Delays ◽

Leibniz Rule ◽

Data Sampling ◽

Control Performance ◽

Sufficient Criterion ◽

Coupled Neural Networks ◽

Synchronization Problem ◽

Sampling Approach

In this paper, the globalO(t-α)synchronization problem is investigated for a class of fractional-order neural networks with time delays. Taking into account both better control performance and energy saving, we make the first attempt to introduce centralized data-sampling approach to characterize theO(t-α)synchronization design strategy. A sufficient criterion is given under which the drive-response-based coupled neural networks can achieve globalO(t-α)synchronization. It is worth noting that, by using centralized data-sampling principle, fractional-order Lyapunov-like technique, and fractional-order Leibniz rule, the designed controller performs very well. Two numerical examples are presented to illustrate the efficiency of the proposed centralized data-sampling scheme.

Download Full-text

Global Stability, Bifurcation, and Chaos Control in a Delayed Neural Network Model

Advances in Artificial Neural Systems ◽

10.1155/2014/369230 ◽

2014 ◽

Vol 2014 ◽

pp. 1-8 ◽

Cited By ~ 2

Author(s):

Amitava Kundu ◽

Pritha Das

Keyword(s):

Neural Network ◽

Network Model ◽

Neural Network Model ◽

Bifurcation Analysis ◽

Time Delays ◽

Chaos Control ◽

Multiple Time ◽

Multiple Time Delays ◽

The Neural Network

Conditions for the global asymptotic stability of delayed artificial neural network model of n (≥3) neurons have been derived. For bifurcation analysis with respect to delay we have considered the model with three neurons and used suitable transformation on multiple time delays to reduce it to a system with single delay. Bifurcation analysis is discussed with respect to single delay. Numerical simulations are presented to verify the analytical results. Using numerical simulation, the role of delay and neuronal gain parameter in changing the dynamics of the neural network model has been discussed.

Download Full-text

QUALITATIVE ANALYSIS OF A NEURAL NETWORK MODEL WITH MULTIPLE TIME DELAYS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127499001103 ◽

1999 ◽

Vol 09 (08) ◽

pp. 1585-1595 ◽

Cited By ~ 64

Author(s):

SUE ANN CAMPBELL ◽

SHIGUI RUAN ◽

JUNJIE WEI

Keyword(s):

Neural Network ◽

Network Model ◽

Neural Network Model ◽

Time Delays ◽

Sufficient Conditions ◽

Positive Equilibrium ◽

Multiple Time ◽

Local Stability Analysis ◽

Multiple Time Delays ◽

Transcendental Functions

We consider a simplified neural network model for a ring of four neurons where each neuron receives two time delayed inputs: One from itself and another from the previous neuron. Local stability analysis of the positive equilibrium leads to a characteristic equation containing products of four transcendental functions. By analyzing the equivalent system of four scalar transcendental equations, we obtain sufficient conditions for the linear stability of the positive equilibrium. Furthermore, we show that a Hopf bifurcation can occur when the positive equilibrium loses stability.

Download Full-text