Fractional Differential Equations

In this paper, the problems of stability and Hopf bifurcation in a class of fractional-order complex-valued single neuron model with time delay are addressed. With the help of the stability theory ...

Stability and Hopf Bifurcation of Fractional-Order Complex-Valued Single Neuron Model with Time Delay

Hopf bifurcation analysis of a complex-valued neural network model with discrete and distributed delays

In this paper, the globally exponential synchronization problem of dynamical networks with nonlinearly coupling function is considered. Hybrid pinning control strategies are established to force the states of the network to follow some objective trajectory. The impulsive pinning controllers are used to control a fringe of nodes at the impulsive instants, while during the impulsive instants, pinning state-feedback controllers are designed to achieve the control objective. Finally, the validity of the developed techniques is evidenced by an illustrative example.

Synchronization of dynamical networks with nonlinearly coupling function under hybrid pinning impulsive controllers

In this paper, a simplified memristor-based fractional-order neural network (MFNN) with discontinuous memductance function is proposed. It is essentially a switched system with irregular switching laws and consists of eight fractional-order neural network (FNN) subsystems. The nonlinear dynamics of the simplified MFNN including equilibrium points and their stability, bifurcation and chaos is investigated analytically and numerically. In particular, the effect of the switching jump on the dynamics of the simplified MFNN is explored for the first time. Taking the fractional order, the memristive connection weight or the switching jump as the bifurcation parameter, the dynamics such as chaotic motion, tangent bifurcation and intermittent chaos is identified over a wide range of some specified parameter. It can be seen that the incorporation of the memristors greatly improves and enriches the dynamics of the corresponding FNN. Different from the period-doubling route to chaos, this paper reveals that the mechanism behind the emergence of chaos for the simplified MFNN is the intermittency route to chaos. In particular, for some typical parameter, the existence of chaotic attractors is verified with the phase portraits, bifurcation diagrams, Poincare sections and maximum Lyapunov exponents, respectively. This paper not only provides a way of designing chaotic MFNN with discontinuous memductance function but also suggests a possible method of generating more complicated chaotic attractors, such as multi-scroll or multi-wing attractors.

Nonlinear dynamics and chaos in a simplified memristor-based fractional-order neural network with discontinuous memductance function

In this paper, a class of three-neuron network with discrete and distributed delays is introduced. We first give a detailed Hopf bifurcation analysis for the proposed network. Choosing the discrete time delay as a bifurcation parameter, the existence of Hopf bifurcation is studied. Moreover, by using the normal form theory and center manifold theorem, the formulae determining the direction of the bifurcations and the stability of the bifurcating periodic solutions are derived. Finally, numerical simulations are presented to demonstrate the effectiveness of our theoretical results.

Stability and Hopf Bifurcation of a Three-Neuron Network with Multiple Discrete and Distributed Delays

In this paper, the synchronization problem of fractional-order complex-valued neural networks with discrete and distributed delays is investigated. Based on the adaptive control and Lyapunov function theory, some sufficient conditions are derived to ensure the states of two fractional-order complex-valued neural networks with discrete and distributed delays achieve complete synchronization rapidly. Finally, numerical simulations are given to illustrate the effectiveness and feasibility of the theoretical results.

Adaptive Synchronization of Fractional-Order Complex-Valued Neural Networks with Discrete and Distributed Delays.

In this paper, the problem of stability for complex-valued neural networks involving both discrete and distributed delays is considered. Assuming that the activation function can be separated into its real and imaginary part, a sufficient condition is proposed for the asymptotical stability of the addressed neural networks by employing some analysis techniques. Finally, a numerical example is presented to demonstrate the effectiveness of the theoretical results.

Li Li

Papers

Hopf bifurcation analysis of a complex-valued neural network model with discrete and distributed delays

Stability and Hopf Bifurcation of a Three-Neuron Network with Multiple Discrete and Distributed Delays

Adaptive Synchronization of Fractional-Order Complex-Valued Neural Networks with Discrete and Distributed Delays.

Stability analysis of a complex-valued neural network with both discrete and distributed delays