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This paper investigates the complex dynamics, synchronization and control of chaos in a system of strongly connected Wilson–Cowan neural oscillators. Some typical synchronized periodic solutions are analyzed by using the Poincaré mapping method, for which bifurcation diagrams are obtained. It is shown that topological change of the synchronization mode is mainly caused and carried out by the Neimark–Sacker bifurcation. Finally, a simple feedback control method is presented for stabilizing an in-phase synchronizing periodic solution embedded in the chaotic attractor of a higher-dimensional model of such coupled neural oscillators.
During the last two decades, chaos of a time-invariant map on a metric space has been extensively studied in the literature. In this paper, by introducing several new concepts, chaos of a time-varying map (i.e., a sequence of time-invariant maps) in a metric space is discussed and, by using these new concepts, broader chaotic discrete dynamical systems are further studied with several new results derived.
For the delayed cellular neural networks, the estimate of exponential convergence rate and exponential stability is considered in this paper. The Lyapunov-Krasovskii functionals combined with linear matrix inequality (LMI) approach are employed to investigate the bound on the cell template and delay-type cell template matrices so that the systems are exponentially stable. Some criteria for the exponential stability which can give information on the delay-dependence are derived.
Naming game simulates the process of naming an objective by a population of agents organized in a certain communication network topology. By pair-wise iterative interactions, the population reaches a consensus state asymptotically. In this paper, we study naming game with communication errors during pair-wise conversations, where errors are represented by error rates in a uniform probability distribution. First, a model of naming game with learning errors in communications (NGLE) is proposed. Then, a strategy for agents to prevent learning errors is suggested. To that end, three typical topologies of communication networks, namely random-graph, small-world and scale-free networks with different parameters, are employed to investigate the effects of various learning errors. Simulation results on these models show that 1) learning errors slightly affect the convergence speed but distinctively increase the requirement for memory of each agent during lexicon propagation; 2) the maximum number of different words held by the whole population increases linearly as the value of the error rate increases; 3) without applying any strategy to eliminate learning errors, there is a threshold value of the learning errors which impairs the convergence. The new findings help to better understand the role of learning errors in naming game as well as human language development from a network science perspective.
Temporal order and synchronization characterized by the rate of firing and its characteristic correlation time are studied in a spatially extended network system, which is locally modelled by a two-dimensional Rulkov map neuron with noise. For intermediate noise levels, noise-induced ordered patterns emerge spatially, which propagate through the neurons in the form of beautiful circular waves. Moreover, noise-induced temporal order and synchronization in this system can be greatly enhanced in the presence of a subthreshold stimulus with the frequency very close to the natural frequency of the map neuron. This shows that random perturbations and subthreshold stimuli play an important role in temporal order and synchronization. There exists an optimal noise level, where the temporal order and synchronization are maximum. However, it is observed that at the same time the spatial circular patterns are destroyed in the course of the enhancement of temporal order and synchronization.
In this paper, the local synchronization of discrete-time complex networks is studied. First, it is shown that for any natural number n, there exists a discrete-time network which has at least disconnected synchronized regions for local synchronization, which implies the possibility of intermittent synchronization behaviors. Different from the continuous-time networks, the existence of an unbounded synchronized region is impossible for discrete-time networks. The convexity of the synchronized regions is also characterized based on the stability of a class of matrix pencils, which is useful for enlarging the stability region so as to improve the network synchronizability.
This paper studies delay-induced quasi-consensus in multi-agent dynamical systems. A linear consensus protocol in second-order dynamics is designed where both the current and delayed position information is utilized. The time delay, in a common perspective, can induce periodic oscillations or even chaos to dynamical systems. However, it is surprisingly found in this paper that quasi-consensus in a multi-agent system cannot be reached without the delayed position information under the given protocol while it can be achieved with a relatively small time delay by appropriately choosing the coupling strength. A necessary and sufficient condition for reaching quasi-consensus in multi-agent dynamical systems is then established. It is further shown that quasi-consensus can be achieved if and only if the time delay is less than a critical value which depends on the coupling strengths and the largest eigenvalue of the Laplacian matrix of the network. Finally, a simulation example is given to illustrate the theoretical analysis.
This paper investigates robust and global exponential synchronizations in an array of nonidentical neural networks with leakage delays and impulsive coupling subject to parametric uncertainties. Some simpler sufficient conditions for synchronization are obtained when uncertainties vanish. A numerical example is given to illustrate the effectiveness of the theoretical results.
In this paper, a linguistic approach to the problem of object recognition is outlined and fuzzy logic solution is given for this formulation. The problem under investigation is divided into two sub-problems: (1) feature extraction from a digitized image, and (2) matching features extracted against a set of pre-defined objects. Using linguistic approach, solving the problem of feature extraction yields a set of linguistic descriptions of an object from a particular digitized image. These descriptions will be matched with known patterns to derive a decision on the shape of the object. The use of fuzzy logic in matching patterns has been shown to provide satisfactory results in Monte Carlo simulations, especially in the case that there is ambiguity in the pictures. This ambiguity is often caused by a lack of extracted features in matching a pattern resulted from some viewpoint at the object or from a picture of poor quality.
In this paper, discretization behaviors of equivalent control based sliding mode control systems with matched uncertainties are studied. Upper bounds for system steady states are established. Some inherent dynamical periodic properties of the systems subject to matched constant and periodic uncertainties are explored. Simulations are presented to verify the theoretical results.
