Synchronization in Coupled Neural Networks With Hybrid Delayed Impulses: Average Impulsive Delay-Gain Method

In this article, we propose a new concept called average impulsive delay-gain (AIDG) for studying the synchronization of coupled neural networks (CNNs). Based on the viewpoints of impulsive control and impulsive perturbation, we establish some globally exponential synchronization criteria for CNNs. Our methods are well-suited for addressing the synchronization problems of systems subject to hybrid delayed impulses with time-varying impulsive delay and gain. Moreover, we prove that the AIDG has both positive and negative effects on synchronization. Compared to existing research, our conclusions are more applicable and less conservative as the considered hybrid delayed impulses involve more flexible cases. Finally, we validate the effectiveness of our proposed results by applying them to small-world and scale-free network models.

Interval Bipartite Synchronization of Multiple Neural Networks in Signed Graphs

Interval bipartite consensus of multiagents described by signed graphs has received extensive concern recently, and the rooted cycles play a critical role in stabilization, while the structurally balanced graphs are essential to achieve bipartite consensus. However, the gauge transformation used in the linear system is no longer feasible in the nonlinear case. This article addresses interval bipartite synchronization of multiple neural networks (NNs) in a signed graph via a Lyapunov-based approach, extending the existing work to a more practical but complicated case. A general matrix M in signed graphs is introduced to construct the novel Lyapunov functions, and sufficient conditions are obtained. We find that the rooted cycles and the structurally balanced graphs are essential to stabilize and achieve bipartite synchronization. More importantly, we discover that the nonrooted cycles are crucial in reaching interval bipartite synchronization, not previously mentioned. Several examples are presented to illustrate interval bipartite synchronization of multiple NNs with signed graphs.

Stability and Hopf bifurcation analysis of a fractional-order ring-hub structure neural network with delays under parameters delay feedback control

In this paper, a fractional-order two delays neural network with ring-hub structure is investigated. Firstly, the stability and the existence of Hopf bifurcation of proposed system are obtained by taking the sum of two delays as the bifurcation parameter. Furthermore, a parameters delay feedback controller is introduced to control successfully Hopf bifurcation. The novelty of this paper is that the characteristic equation corresponding to system has two time delays and the parameters depend on one of them. Selecting two time delays as the bifurcation parameters simultaneously, stability switching curves in $ (\tau_{1}, \tau_{2}) $ plane and crossing direction are obtained. Sufficient criteria for the stability and the existence of Hopf bifurcation of controlled system are given. Ultimately, numerical simulation shows that parameters delay feedback controller can effectively control Hopf bifurcation of system.

Laser Spot Detection Based on Reaction Diffusion

Center-location of a laser spot is a problem of interest when the laser is used for processing and performing measurements. Measurement quality depends on correctly determining the location of the laser spot. Hence, improving and proposing algorithms for the correct location of the spots are fundamental issues in laser-based measurements. In this paper we introduce a Reaction Diffusion (RD) system as the main computational framework for robustly finding laser spot centers. The method presented is compared with a conventional approach for locating laser spots, and the experimental results indicate that RD-based computation generates reliable and precise solutions. These results confirm the flexibility of the new computational paradigm based on RD systems for addressing problems that can be reduced to a set of geometric operations.

Synchronization of memristor-based recurrent neural networks with two delay components based on second-order reciprocally convex approach

We extend the notion of Synchronization of memristor-based recurrent neural networks with two delay components based on second-order reciprocally convex approach. Some sufficient conditions are obtained to guarantee the synchronization of the memristor-based recurrent neural networks via delay-dependent output feedback controller in terms of linear matrix inequalities (LMIs). The activation functions are assumed to be of further common descriptions, which take a broad view and recover many of those existing methods. A Lyapunov-Krasovskii functional (LKF) with triple-integral terms is addressed in this paper to condense conservatism in the synchronization of systems with additive time-varying delays. Jensen's inequality is applied in partitioning the double integral terms in the derivation of LMIs and then a new kind of linear combination of positive functions weighted by the inverses of squared convex parameters has emerged. Meanwhile, this paper puts forward a well-organized method to manipulate such a combination by extending the lower bound lemma. The obtained conditions not only have less conservatism but also less decision variables than existing results. Finally, numerical results and its simulations are given to show the effectiveness of the proposed memristor-based synchronization control scheme.

Synchronization of Coupled Neutral-Type Neural Networks With Jumping-Mode-Dependent Discrete and Unbounded Distributed Delays

In this paper, the synchronization problem is studied for an array of N identical delayed neutral-type neural networks with Markovian jumping parameters. The coupled networks involve both the mode-dependent discrete-time delays and the mode-dependent unbounded distributed time delays. All the network parameters including the coupling matrix are also dependent on the Markovian jumping mode. By introducing novel Lyapunov-Krasovskii functionals and using some analytical techniques, sufficient conditions are derived to guarantee that the coupled networks are asymptotically synchronized in mean square. The derived sufficient conditions are closely related with the discrete-time delays, the distributed time delays, the mode transition probability, and the coupling structure of the networks. The obtained criteria are given in terms of matrix inequalities that can be efficiently solved by employing the semidefinite program method. Numerical simulations are presented to further demonstrate the effectiveness of the proposed approach.

Partial synchronization in stochastic dynamical networks with switching communication channels

In this paper, the partial synchronization problem of stochastic dynamical networks (SDNs) is investigated. Unlike the existing models, the SDN considered in this paper suffers from a class of communication constraint-only part of nodes' states can be transmitted. Thus, less nodes' states can be used to synchronize the SDN, which makes the analysis of the synchronization problem much harder. A set of channel matrices are introduced to reflect such kind of constraint. Furthermore, due to unpredictable environmental changes, the channel matrices can switch among some communication modes. The switching considered here is governed by a Markov process. To overcome the difficulty, a regrouping method is employed to derive our main results. The obtained conditions guarantee that partial synchronization can be achieved for SDNs under switching communication constraint. Finally, numerical examples are given to illustrate the effectiveness of the theoretical results and how the communication constraint influences synchronization result.

Robust synchronization for 2-D discrete-time coupled dynamical networks

In this paper, a new synchronization problem is addressed for an array of 2-D coupled dynamical networks. The class of systems under investigation is described by the 2-D nonlinear state space model which is oriented from the well-known Fornasini-Marchesini second model. For such a new 2-D complex network model, both the network dynamics and the couplings evolve in two independent directions. A new synchronization concept is put forward to account for the phenomenon that the propagations of all 2-D dynamical networks are synchronized in two directions with influence from the coupling strength. The purpose of the problem addressed is to first derive sufficient conditions ensuring the global synchronization and then extend the obtained results to more general cases where the system matrices contain either the norm-bounded or the polytopic parameter uncertainties. An energy-like quadratic function is developed, together with the intensive use of the Kronecker product, to establish the easy-to-verify conditions under which the addressed 2-D complex network model achieves global synchronization. Finally, a numerical example is given to illustrate the theoretical results and the effectiveness of the proposed synchronization scheme.

Exponential lag synchronization for neural networks with mixed delays via periodically intermittent control

In this paper, the exponential lag synchronization for a class of neural networks with discrete delays and distributed delays is studied via periodically intermittent control for the first time. Some novel and useful criteria are derived by using mathematical induction method and the analysis technique which are different from the methods employed in correspondingly previous works. Finally, some numerical simulations are given to demonstrate the effectiveness of the proposed control methods.

Log-domain implementation of complex dynamics reaction-diffusion neural networks

We have identified a second-order reaction-diffusion differential equation able to reproduce through parameter setting different complex spatio-temporal behaviors. We have designed a log-domain hardware that implements the spatially discretized version of the selected reaction-diffusion equation. The logarithmic compression of the state variables allows several decades of variation of these state variables within subthreshold operation of the MOS transistors. Furthermore, as all the equation parameters are implemented as currents, they can be adjusted several decades. As a demonstrator, we have designed a chip containing a linear array of ten second-order dynamics coupled cells. Using this hardware, we have experimentally reproduced two complex spatio-temporal phenomena: the propagation of travelling waves and of trigger waves, as well as isolated oscillatory cells.

Soft tissue modelling through autowaves for surgery simulation

Modelling of soft tissue deformation is of great importance to virtual reality based surgery simulation. This paper presents a new methodology for simulation of soft tissue deformation by drawing an analogy between autowaves and soft tissue deformation. The potential energy stored in a soft tissue as a result of a deformation caused by an external force is propagated among mass points of the soft tissue by non-linear autowaves. The novelty of the methodology is that (i) autowave techniques are established to describe the potential energy distribution of a deformation for extrapolating internal forces, and (ii) non-linear materials are modelled with non-linear autowaves other than geometric non-linearity. Integration with a haptic device has been achieved to simulate soft tissue deformation with force feedback. The proposed methodology not only deals with large-range deformations, but also accommodates isotropic, anisotropic and inhomogeneous materials by simply changing diffusion coefficients.

Vibrational resonance in a noise-induced structure

We report on the effect of vibrational resonance in a spatially extended system of coupled noisy oscillators under the action of two periodic forces, a low-frequency one (signal) and a high-frequency one (carrier). Vibrational resonance manifests itself in the fact that for optimally selected values of high-frequency force amplitude, the response of the system to a low-frequency signal is optimal. This phenomenon is a synthesis of two effects, a noise-induced phase transition leading to bistability, and a conventional vibrational resonance, resulting in the optimization of signal processing. Numerical simulations, which demonstrate this effect for an extended system, can be understood by means of a zero-dimensional "effective" model. The behavior of this "effective" model is also confirmed by an experimental realization of an electronic circuit.

Chemical reaction-diffusion implementation of finding the shortest paths in a labyrinth

An experimental technique for finding the shortest paths in a labyrinth is elaborated on based on chemical reaction-diffusion media. The system designed has hybrid architecture that combines an information-processing reaction-diffusion medium performing operations of high computational complexity with a digital computer carrying out supplementary operations. Two principal points are assumed as a basis for this design. They are the following: a light-sensitive Belousov-Zhabotinsky-type reagent chosen as a reaction-diffusion medium that offers the opportunity to simulate a labyrinth and spread wave evolution by its images stored in the medium; fast light-induced phase wave processes that spread through the labyrinth in seconds instead of the dozens of minutes typical of trigger waves inherent in reaction-diffusion media. Images of consecutive wave-spreading steps are stored in the memory of a digital computer. These images are used to determine the shortest paths based on the additional procedure of testing for the connectedness of labyrinth fragments.

Nonlinear waves, patterns and spatio-temporal chaos in cellular neural networks

Spatio-temporal pattern formation occurring in discretely coupled nonlinear dynamical systems has been studied numerically. In this paper, we review the possibilities of using arrays of discretely coupled nonlinear electronic circuits to study these systems. Spiral wave initiation and Turing pattern formation are some of the examples. Sidewall forcing of Turing patterns is shown to be capable of driving the system into a perfect spatial organization, namely, a rhombic pattern, where no defects occur. The dynamics of the two layers supporting Turing and Hopf modes, respectively, is analysed as a function of the coupling strength between them. The competition between these two modes is shown to increase with the diffusion between layers. As well, the coexistence of low- and high-dimensional spatio-temporal chaos is shown to occur in one-dimensional arrays.