Nonlinear Dynamics and Chaos in Fractional-Order Hopfield Neural Networks with Delay
نویسندگان
چکیده
A fractional-order two-neuron Hopfield neural network with delay is proposed based on the classic well-known Hopfield neural networks, and further, the complex dynamical behaviors of such a network are investigated. A great variety of interesting dynamical phenomena, including single-periodic,multiple-periodic, and chaoticmotions, are found to exist.The existence of chaotic attractors is verified by the bifurcation diagram and phase portraits as well.
منابع مشابه
Nonlinear Dynamics and Symbolic Dynamics of Neural Networks
A piecewise linear equation is proposed as a method of analysis of mathematical models of neural networks. A symbolic representation of the dynamics in this equation is given as a directed graph on an N-dimensional hypercube. This provides a formal link with discrete neural networks such as the original Hopfield models. Analytic criteria are given to establish steady states and limit cycle osci...
متن کاملExistence and Global Stability of Periodic Solution for Delayed Discrete High-order Hopfield-type Neural Networks
It is well known that studies on neural dynamical systems not only involve discussion of stability property, but also involve other dynamics behaviors such as periodic oscillatory, bifurcation and chaos. In many applications, the property of periodic oscillatory solutions are of great interest. For example, the human brain has been in periodic oscillatory or chaos state, hence it is of prime im...
متن کاملAdaptive Leader-Following and Leaderless Consensus of a Class of Nonlinear Systems Using Neural Networks
This paper deals with leader-following and leaderless consensus problems of high-order multi-input/multi-output (MIMO) multi-agent systems with unknown nonlinear dynamics in the presence of uncertain external disturbances. The agents may have different dynamics and communicate together under a directed graph. A distributed adaptive method is designed for both cases. The structures of the contro...
متن کاملSome Remarkable Properties of a Hopfield Neural Network with Time Delay
It is known that an analog Hopfield neural network with time delay can generate the outputs which are similar to the human electroencephalogram. To gain deeper insights into the mechanisms of rhythm generation by the Hopfield neural networks and to study the effects of noise on their activities, we investigated the behaviors of the networks with symmetric and asymmetric interneuron connections....
متن کاملFinite Time Mix Synchronization of Delay Fractional-Order Chaotic Systems
Chaos synchronization of coupled fractional order differential equation is receiving increasing attention because of its potential applications in secure communications and control processing. The aim of this paper is synchronization between two identical or different delay fractional-order chaotic systems in finite time. At first, the predictor-corrector method is used to obtain the solutions ...
متن کامل