A New Memristive Neuron Map Model and Its Network’s Dynamics under Electrochemical Coupling

A memristor is a vital circuit element that can mimic biological synapses. This paper proposes the memristive version of a recently proposed map neuron model based on the phase space. The dynamic of the memristive map model is investigated by using bifurcation and Lyapunov exponents’ diagrams. The results prove that the memristive map can present different behaviors such as spiking, periodic bursting, and chaotic bursting. Then, a ring network is constructed by hybrid electrical and chemical synapses, and the memristive neuron models are used to describe the nodes. The collective behavior of the network is studied. It is observed that chemical coupling plays a crucial role in synchronization. Different kinds of synchronization, such as imperfect synchronization, complete synchronization, solitary state, two-cluster synchronization, chimera, and nonstationary chimera, are identified by varying the coupling strengths.

Synchronization or cluster synchronization in coupled Van der Pol oscillators networks with different topological types

In this paper, we try to discuss the mechanism of synchronization or cluster synchronization in the coupled Van der Pol oscillator networks with different topology types by using the theory of rotating periodic solutions. The synchronous solutions here are transformed into rotating periodic solutions of some dynamical systems. By analyzing the bifurcation of rotating periodic solutions, the critical conditions of synchronous solutions are given in three different networks. We use the rotating periodic matrix in the rotating periodic theory to judge various types of synchronization phenomena, such as complete synchronization, anti-phase synchronization, periodic synchronization, or cluster synchronization. All rotating periodic matrices which satisfy the exchange invariance of multiple oscillators form special groups in these networks. By using the conjugate classes of these groups, we obtain various possible synchronization solutions in the three networks. In particular, we find symmetry has different effects on synchronization in different networks. The network with better symmetry has more elements in the corresponding group, which may have more types of synchronous solutions. However, different types of symmetry may get the same type of synchronous solutions or different types of synchronous solutions, depending on whether their corresponding rotating periodic matrices are similar.

Cluster control of complex cyber-physical systems

To our minds, the real world appears as a composition of different interacting entitites, which demonstrate complex behavior. In the current paper, we primarly aim to study such networked systems by developing corresponding approaches to modeling them, given a class of tasks. We derive it from the primary concept of information and a system, with corresponding dynamics emerging from interactions between system components. As we progress through the study, we discover three possible levels of certain synchronous pattern composition in complex systems: microscopic (the level of elementary components), mesoscopic (the level of clusters), and macroscopic (the level of the whole system). Above all, we focus on the clusterization phenomenon, which allows to reduce system complexity by regarding only a small number of stable manifolds, corresponding to cluster synchronization of system component states—as opposed to regarding the system as a whole or each elementary component separately. Eventually, we demonstrate how an optimization problem for cluster control synthesis can be formulated for a simple discrete linear system with clusterization.

Modeling and Dynamical Analysis of Multi-Area Network with a Third-Order Chaotic Power System

The synchronization of states is important to sustain the energy of consumers at any given time for power networks. This paper focuses on the multi-area power network model and then analyzes the cluster synchronization of this kind of network comprised of a third-order chaotic power system. Specifically, we investigate the rich dynamic properties of the single third-order power system. Furthermore, the multi-area network model with the chaotic power system is proposed and the adaptive controller is designed to achieve cluster synchronization. Combining analytical considerations with numerical simulations on a small-scale network, we address the cluster synchronous performance in the multi-area power network. Therefore, our results can provide a basic physical picture for power system dynamics and enable us to further understand the complex dynamical behavior in the multi-area power network.

Cluster Synchronization in Variable-Order Fractional Community Network via Intermittent Control

In this paper, the cluster synchronization of a variable-order fractional community network with nonidentical dynamics is investigated. For achieving the cluster synchronization, intermittent controllers are designed, and the sufficient conditions with respect to system parameters, intermittent control instants and control gains are derived based on stability theory of fractional-order system and linear matrix inequalities (LMIs). To avoid verifying the LMIs, a corresponding simple corollary is provided. Finally, a numerical example is performed to verify the derived result.