Adaptive pinning cluster synchronization of a stochastic reaction-diffusion complex network

This work aims to achieve cluster synchronization of a complex network by some pinning control strategies. Firstly, the network not only is affected by the reaction-diffusion and the directed coupling phenomena, but also is disturbed by the stochastic noise and Markovian switching. Secondly, switched constant gain pinning, centralized and decentralized adaptive pinning are proposed respectively to realize the cluster synchronization of the considered network. In these adaptive pinning controllers, the control gain and coupling strength can been adjusted automatically while only a part of the nodes are controlled. Thirdly, the target state of cluster synchronization is taken as the average state related to the directed topology of all nodes in the same cluster, and does not need to be given separately as an isolated node. Finally, to verify the theoretical results, some simulations of directed coupled reaction-diffusion neural networks with stochastic noise and Markovian switching are given.

Edge-Based Fractional-Order Adaptive Strategies for Synchronization of Fractional-Order Coupled Networks With Reaction-Diffusion Terms

In this paper, spatial diffusions are introduced to fractional-order coupled networks and the problem of synchronization is investigated for fractional-order coupled neural networks with reaction-diffusion terms. First, a new fractional-order inequality is established based on the Caputo partial fractional derivative. To realize asymptotical synchronization, two types of adaptive coupling weights are considered, namely: 1) coupling weights only related to time and 2) coupling weights dependent on both time and space. For each type of coupling weights, based on local information of the node's dynamics, an edge-based fractional-order adaptive law and an edge-based fractional-order pinning adaptive scheme are proposed. Furthermore, some new analytical tools, including the method of contradiction, L'Hopital rule, and Barbalat lemma are developed to establish adaptive synchronization criteria of the addressed networks. Finally, an example with numerical simulations is provided to illustrate the validity and effectiveness of the theoretical results.

Spacial sampled-data control for H∞ output synchronization of directed coupled reaction-diffusion neural networks with mixed delays

This work investigates the H_∞ output synchronization (HOS) of the directed coupled reaction-diffusion (R-D) neural networks (NNs) with mixed delays. Firstly, a model of the directed state coupled R-D NNs is introduced, which not only contains some discrete and distributed time delays, but also obeys a mixed Dirichlet-Neumann boundary condition. Secondly, a spacial sampled-data controller is proposed to achieve the HOS of the considered networks. This type of controller can reduce the update rate in the process of control by measuring the state of networks at some fixed sampling points in the space region. Moreover, some criteria for the HOS are established by designing an appropriate Lyapunov functional, and some quantitative relations between diffusion coefficients, mixed delays, coupling strength and control parameters are given accurately by these criteria. Thirdly, the case of directed spatial diffusion coupled networks is also studied and, the following finding is obtained: the spatial diffusion coupling can suppress the HOS while the state coupling can promote it. Finally, one example is simulated as the verification of the theoretical results.

Soft tissue deformation modelling through neural dynamics-based reaction-diffusion mechanics

Soft tissue deformation modelling forms the basis of development of surgical simulation, surgical planning and robotic-assisted minimally invasive surgery. This paper presents a new methodology for modelling of soft tissue deformation based on reaction-diffusion mechanics via neural dynamics. The potential energy stored in soft tissues due to a mechanical load to deform tissues away from their rest state is treated as the equivalent transmembrane potential energy, and it is distributed in the tissue masses in the manner of reaction-diffusion propagation of nonlinear electrical waves. The reaction-diffusion propagation of mechanical potential energy and nonrigid mechanics of motion are combined to model soft tissue deformation and its dynamics, both of which are further formulated as the dynamics of cellular neural networks to achieve real-time computational performance. The proposed methodology is implemented with a haptic device for interactive soft tissue deformation with force feedback. Experimental results demonstrate that the proposed methodology exhibits nonlinear force-displacement relationship for nonlinear soft tissue deformation. Homogeneous, anisotropic and heterogeneous soft tissue material properties can be modelled through the inherent physical properties of mass points. Graphical abstract Soft tissue deformation modelling with haptic feedback via neural dynamics-based reaction-diffusion mechanics.

ChainMail based neural dynamics modeling of soft tissue deformation for surgical simulation

BACKGROUND

Realistic and real-time modeling and simulation of soft tissue deformation is a fundamental research issue in the field of surgical simulation.

OBJECTIVE

In this paper, a novel cellular neural network approach is presented for modeling and simulation of soft tissue deformation by combining neural dynamics of cellular neural network with ChainMail mechanism.

METHOD

The proposed method formulates the problem of elastic deformation into cellular neural network activities to avoid the complex computation of elasticity. The local position adjustments of ChainMail are incorporated into the cellular neural network as the local connectivity of cells, through which the dynamic behaviors of soft tissue deformation are transformed into the neural dynamics of cellular neural network.

RESULTS

Experiments demonstrate that the proposed neural network approach is capable of modeling the soft tissues' nonlinear deformation and typical mechanical behaviors.

CONCLUSIONS

The proposed method not only improves ChainMail's linear deformation with the nonlinear characteristics of neural dynamics but also enables the cellular neural network to follow the principle of continuum mechanics to simulate soft tissue deformation.

Mittag-Leffler synchronization of fractional neural networks with time-varying delays and reaction-diffusion terms using impulsive and linear controllers

In this paper, we propose a fractional-order neural network system with time-varying delays and reaction-diffusion terms. We first develop a new Mittag-Leffler synchronization strategy for the controlled nodes via impulsive controllers. Using the fractional Lyapunov method sufficient conditions are given. We also study the global Mittag-Leffler synchronization of two identical fractional impulsive reaction-diffusion neural networks using linear controllers, which was an open problem even for integer-order models. Since the Mittag-Leffler stability notion is a generalization of the exponential stability concept for fractional-order systems, our results extend and improve the exponential impulsive control theory of neural network system with time-varying delays and reaction-diffusion terms to the fractional-order case. The fractional-order derivatives allow us to model the long-term memory in the neural networks, and thus the present research provides with a conceptually straightforward mathematical representation of rather complex processes. Illustrative examples are presented to show the validity of the obtained results. We show that by means of appropriate impulsive controllers we can realize the stability goal and to control the qualitative behavior of the states. An image encryption scheme is extended using fractional derivatives.

Impulsive Synchronization of Reaction-Diffusion Neural Networks With Mixed Delays and Its Application to Image Encryption

This paper presents a new impulsive synchronization criterion of two identical reaction-diffusion neural networks with discrete and unbounded distributed delays. The new criterion is established by applying an impulse-time-dependent Lyapunov functional combined with the use of a new type of integral inequality for treating the reaction-diffusion terms. The impulse-time-dependent feature of the proposed Lyapunov functional can capture more hybrid dynamical behaviors of the impulsive reaction-diffusion neural networks than the conventional impulse-time-independent Lyapunov functions/functionals, while the new integral inequality, which is derived from Wirtinger's inequality, overcomes the conservatism introduced by the integral inequality used in the previous results. Numerical examples demonstrate the effectiveness of the proposed method. Later, the developed impulsive synchronization method is applied to build a spatiotemporal chaotic cryptosystem that can transmit an encrypted image. The experimental results verify that the proposed image-encrypting cryptosystem has the advantages of large key space and high security against some traditional attacks.

Self-Organizing Map With Time-Varying Structure to Plan and Control Artificial Locomotion

This paper presents an algorithm, self-organizing map-state trajectory generator (SOM-STG), to plan and control legged robot locomotion. The SOM-STG is based on an SOM with a time-varying structure characterized by constructing autonomously close-state trajectories from an arbitrary number of robot postures. Each trajectory represents a cyclical movement of the limbs of an animal. The SOM-STG was designed to possess important features of a central pattern generator, such as rhythmic pattern generation, synchronization between limbs, and swapping between gaits following a single command. The acquisition of data for SOM-STG is based on learning by demonstration in which the data are obtained from different demonstrator agents. The SOM-STG can construct one or more gaits for a simulated robot with six legs, can control the robot with any of the gaits learned, and can smoothly swap gaits. In addition, SOM-STG can learn to construct a state trajectory form observing an animal in locomotion. In this paper, a dog is the demonstrator agent.

Delay-dependent stability criteria for reaction–diffusion neural networks with time-varying delays

This paper studies the global asymptotic stability problem of a class of reaction–diffusion neural networks with time-varying delays. To overcome the difficulty caused by the partial differential term, a novel Lyapunov–Krasovskii functional is proposed, and a partial differential equation technique together with a linear operator approach are also applied to obtain the delay-dependent stability criteria, which are less conservative than the existing results. Finally, simulation examples are given to verify and illustrate the theoretical analysis.

Cluster synchronization in networks of coupled nonidentical dynamical systems

In this paper, we study cluster synchronization in networks of coupled nonidentical dynamical systems. The vertices in the same cluster have the same dynamics of uncoupled node system but the uncoupled node systems in different clusters are different. We present conditions guaranteeing cluster synchronization and investigate the relation between cluster synchronization and the unweighted graph topology. We indicate that two conditions play key roles for cluster synchronization: the common intercluster coupling condition and the intracluster communication. From the latter one, we interpret the two cluster synchronization schemes by whether the edges of communication paths lie in inter- or intracluster. By this way, we classify clusters according to whether the communications between pairs of vertices in the same cluster still hold if the set of edges inter- or intracluster edges is removed. Also, we propose adaptive feedback algorithms to adapting the weights of the underlying graph, which can synchronize any bi-directed networks satisfying the conditions of common intercluster coupling and intracluster communication. We also give several numerical examples to illustrate the theoretical results.

A method to model neuron activity

This paper presents a model to simulate the activity of excitable membrane displaying Hodgkin and Huxley (H-H)-type kinetics implemented using the general-purpose circuit analysis program PSPICE. The H-H equations are represented by electrical equivalent circuit elements and the model is validated by comparison with published theoretical and measured data. The model is very easy to use and can be inserted as a sub-circuit into PSPICE simulations of more complex neural systems.

Adaptive dynamical networks via neighborhood information: synchronization and pinning control

In this paper, we introduce a model of an adaptive dynamical network by integrating the complex network model and adaptive technique. In this model, the adaptive updating laws for each vertex in the network depend only on the state information of its neighborhood, besides itself and external controllers. This suggests that an adaptive technique be added to a complex network without breaking its intrinsic existing network topology. The core of adaptive dynamical networks is to design suitable adaptive updating laws to attain certain aims. Here, we propose two series of adaptive laws to synchronize and pin a complex network, respectively. Based on the Lyapunov function method, we can prove that under several mild conditions, with the adaptive technique, a connected network topology is sufficient to synchronize or stabilize any chaotic dynamics of the uncoupled system. This implies that these adaptive updating laws actually enhance synchronizability and stabilizability, respectively. We find out that even though these adaptive methods can succeed for all networks with connectivity, the underlying network topology can affect the convergent rate and the terminal average coupling and pinning strength. In addition, this influence can be measured by the smallest nonzero eigenvalue of the corresponding Laplacian. Moreover, we provide a detailed study of the influence of the prior parameters in this adaptive laws and present several numerical examples to verify our theoretical results and further discussion.

Simulations of the behavior of synaptically driven neurons via time-invariant circuit models

This paper describes computer simulations of the behavior of Hodgkin-Huxley neurons, based on a redefinition of membrane and synaptic connections as time-invariant circuit elements. Examples are given showing that this self-consistent equivalent circuit representation allows very efficient computer simulations and could facilitate the introduction of detailed biological neurons into formal neural networks.