Multisynchronization of Coupled Heterogeneous Genetic Oscillator Networks via Partial Impulsive Control

Multistability and fixed-time multisynchronization of switched neural networks with state-dependent switching rules

This paper presents theoretical results on the multistability and fixed-time synchronization of switched neural networks with multiple almost-periodic solutions and state-dependent switching rules. It is shown herein that the number, location, and stability of the almost-periodic solutions of the switched neural networks can be characterized by making use of the state-space partition. Two sets of sufficient conditions are derived to ascertain the existence of 3n exponentially stable almost-periodic solutions. Subsequently, this paper introduces the novel concept of fixed-time multisynchronization in switched neural networks associated with a range of almost-periodic parameters within multiple stable equilibrium states for the first time. Based on the multistability results, it is demonstrated that there are 3n synchronization manifolds, wherein n is the number of neurons. Additionally, an estimation for the settling time required for drive-response switched neural networks to achieve synchronization is provided. It should be noted that this paper considers stable equilibrium points (static multisynchronization), stable almost-periodic orbits (dynamical multisynchronization), and hybrid stable equilibrium states (hybrid multisynchronization) as special cases of multistability (multisynchronization). Two numerical examples are elaborated to substantiate the theoretical results.

Pinning multisynchronization of delayed fractional-order memristor-based neural networks with nonlinear coupling and almost-periodic perturbations

This paper concerns the multisynchronization issue for delayed fractional-order memristor-based neural networks with nonlinear coupling and almost-periodic perturbations. First, the coexistence of multiple equilibrium states for isolated subnetwork is analyzed. By means of state-space decomposition, fractional-order Halanay inequality and Caputo derivative properties, the novel algebraic sufficient conditions are derived to ensure that the addressed networks with arbitrary activation functions have multiple locally stable almost periodic orbits or equilibrium points. Then, based on the obtained multistability results, a pinning control strategy is designed to realize the multisynchronization of the N coupled networks. By the aid of graph theory, depth first search method and pinning control law, some sufficient conditions are formulated such that the considered neural networks can possess multiple synchronization manifolds. Finally, the multistability and multisynchronization performance of the considered neural networks with different activation functions are illustrated by numerical examples.

Reliable impulsive synchronization for fuzzy neural networks with mixed controllers

This work studies the synchronization of the master-slave (MS) fuzzy neural networks (FNNs) with random actuator failure, where the state information of the master FNNs can not be obtained directly. To reduce the loads of the communication channel and the controller, the simultaneously impulsive driven strategy of the communication channel and the controller is proposed. On the basis of the received measurements of the master FNNs, the mixed controller consisting of observer based controller and the static controller is designed. The randomly occurred actuator failure is also considered. According to the Lyapunov method, the sufficient conditions are achieved to ensure the synchronization of the MS FNNs, and the controller gains are designed by using the obtained results. The validity of the derived results is illustrated by a numerical example.

Dynamical and static multisynchronization analysis for coupled multistable memristive neural networks with hybrid control

This paper investigates the dynamical multisynchronization (DMS) and static multisynchronization (SMS) problems for a class of delayed coupled multistable memristive neural networks (DCMMNNs) via a novel hybrid controller which includes delayed impulsive control and state feedback control. Based on the state-space partition method and the geometrical properties of the activation function, each subnetwork has multiple locally exponential stable equilibrium states. By employing a new Halanay-type inequality and the impulsive control theory, some new linear matrix inequalities (LMIs)-based sufficient conditions are proposed. It is shown that the delayed impulsive control with suitable impulsive interval and allowable time-varying delay can still guarantee the DMS and SMS of DCMMNNs. Finally, a numerical example is presented to illustrate the effectiveness of the hybrid controller.

Stochastic quasi-synchronization of heterogeneous delayed impulsive dynamical networks via single impulsive control

This paper investigates the quasi-synchronization problem of the stochastic heterogeneous complex dynamical networks with impulsive couplings and multiple time-varying delays. It is shown that this kind of dynamical networks can achieve exponential quasi-synchronization by exerting impulsive control added on only one chosen pinning node. By employing the Lyapunov stability theory, some sufficient criteria on quasi-synchronization for this dynamical network are established, revealing the relationship between the quasi-synchronization performance and the stochastic perturbations as well as the frequency and strength of impulsive coupling. Finally, some numerical examples are used to illustrate the effectiveness of the main results.

Average Quasi-Consensus Algorithm for Distributed Constrained Optimization: Impulsive Communication Framework

This paper presents the impulsive average quasi-consensus algorithm for distributed constrained convex optimization. First, the constrained optimization problem can be transformed into an unconstrained problem using the interior point method, and then a distributed algorithm is modeled by means of impulsive differential equation. In the framework of the continuous-time gradient method and algebraic graph theory, each agent can deal with one local objective function with local constraints. At the impulsive instants, each agent can communicate with its neighboring agents over the network. Under certain conditions, the impulsive average quasi-consensus is achieved. It is shown that the state of average quasi-consensus is the optimal solution of the aforementioned unconstrained optimization problem, and the state of each agent can also reach the neighborhood of the optimal solution. Finally, two numerical examples show the effectiveness of the proposed impulsive average quasi-consensus algorithm. Moreover, the feasibility of the approach is verified by an application to one sensor network localization problem.

Dynamical and Static Multisynchronization of Coupled Multistable Neural Networks via Impulsive Control

This paper investigates the dynamical multisynchronization and static multisynchronization problem for delayed coupled multistable neural networks with fixed and switching topologies. To begin with, a class of activation functions as well as several sufficient conditions are introduced to ensure that every subnetwork has multiple equilibrium states. By constructing an appropriate Lyapunov function and by employing impulsive control theory and the average impulsive interval method, several sufficient conditions for multisynchronization in terms of linear matrix inequalities (LMIs) are obtained. Moreover, a unified impulsive controller is designed by means of the established LMIs. Finally, a numerical example is presented to demonstrate the effectiveness of the presented impulsive control strategy.

Theoretical Study of Oscillator Neurons in Recurrent Neural Networks

Neurons in a network can be both active or inactive. Given a subset of neurons in a network, is it possible for the subset of neurons to evolve to form an active oscillator by applying some external periodic stimulus? Furthermore, can these oscillator neurons be observable, that is, is it a stable oscillator? This paper explores such possibility, finding that an important property: any subset of neurons can be intermittently co-activated to form a stable oscillator by applying some external periodic input without any condition. Thus, the existing of intermittently active oscillator neurons is an essential property possessed by the networks. Moreover, this paper shows that, under some conditions, a subset of neurons can be fully co-activated to form a stable oscillator. Such neurons are called selectable oscillator neurons. Necessary and sufficient conditions are established for a subset of neurons to be selectable oscillator neurons in linear threshold recurrent neuron networks. It is proved that a subset of neurons forms selectable oscillator neurons if and only if the real part of each eigenvalue of the associated synaptic connection weight submatrix of the network is not larger than one. This simple condition makes the concept of selectable oscillator neurons tractable. The selectable oscillator neurons can be regarded as memories stored in the synaptic connections of networks, which enables to find a new perspective of memories in neural networks, different from the equilibrium-type attractors.