Spatiotemporal chaos synchronization between uncertain complex networks with diverse structures

Spatiotemporal chaos synchronization between uncertain complex networks with diverse structures is investigated. The identification law of unknown parameters and the adaptive law of the configuration matrix element in state equations of network nodes are determined based on stability theory, and the conditions of realizing spatiotemporal chaos synchronization between uncertain complex networks with different structures are discussed and obtained. Further, the Fisher–Kolmogorov system with spatiotemporal chaotic behavior is taken as the nodes of drive and response networks to imitate the experiment. It is found that the synchronization performance between two networks is very stable.     

Parameter identification and synchronization of spatiotemporal chaos in uncertain complex network

Synchronization and parameter identification of a unidirectional star-network constructed by discrete spatiotemporal chaos systems with unknown parameters are studied. The synchronization principle of the network and design method of parameter recognition law are introduced. The function to be determined in the parameter recognition law and the range of adjusting parameter are obtained based on Lyapunov stability theory. Not only global synchronization of the network is realized, but also the unknown parameters in spatiotemporal chaos systems at the nodes of the network are identified. Discrete laser spatiotemporal chaos model is taken as each node of the network, and simulation results show the effectiveness of the synchronization principle and parameter recognition law.     

Generalized synchronization of spatiotemporal chaos in a weighted complex network

The nodes of the network are composed of the spatiotemporal chaos systems. The relations between the nodes are built through a weighted connection and the nonlinear terms of the chaos systems themselves are taken as coupling functions. The structure of the coupling functions between the connected nodes and the range of the control gain are obtained based on Lyapunov stability theory. It is proven that generalized chaos synchronization of the weight complex network can be realized even if the coupling strength between the nodes is adopted as any weight value. Subsequently, the catalytic reaction diffusion system which has spatiotemporal chaos behavior is taken as example, and simulation results show the effectiveness of the synchronization principle.     

Outer synchronization of uncertain small-world networks via adaptive sliding mode control

The outer synchronization of irregular coupled complex networks is investigated with nonidentical topological structures. The switching gain is estimated by an adaptive technique, and a sliding mode controller is designed to satisfy the sliding condition. The outer synchronization between two irregular coupled complex networks with different initial conditions is implemented via the designed controllers with the corresponding parameter update laws. The chaos synchronization of two small-world networks consisting of N uncertain identical Lorenz systems is achieved to demonstrate the applications of the proposed approach.     

Sliding mode synchronization between uncertain Watts-Strogatz small-world spatiotemporal networks

Based on the topological characteristics of small-world networks, a nonlinear sliding mode controller is designed to minimize the effects of internal parameter uncertainties. To qualify the effects of uncertain parameters in the response networks, some effective recognition rates are designed so as to achieve a steady value in the extremely fast simulation time period. Meanwhile, the Fisher-Kolmogorov and Burgers spatiotemporal chaotic systems are selected as the network nodes for constructing a drive and a response network, respectively. The simulation results confirm that the developed sliding mode could realize the effective synchronization problem between the spatiotemporal networks, and the outer synchronization is still achieved timely even when the connection probability of the small-world networks changes.     

Spatiotemporal and synchronous chaos in accumulated coupled map lattice

The onset of spatiotemporal chaos in coupled map lattice (CML) with a new coupling scheme called accumulated CML is studied in this paper. A rigorous proof of the existence of chaos in the sense of Li–Yorke is presented. Also the range of the coupling strength in which global synchronization can be obtained is calculated by stability analysis of the synchronized state. Finally, the positivity of Lyapunov exponents confirms the existence of chaos.     

Effects of information transmission delay and channel blocking on synchronization in scale-free Hodgkin-Huxley neuronal networks

In this paper,we investigate the evolution of spatiotemporal patterns and synchronization transitions in dependence on the information transmission delay and ion channel blocking in scale-free neuronal networks.As the underlying model of neuronal dynamics,we use the Hodgkin-Huxley equations incorporating channel blocking and intrinsic noise.It is shown that delays play a significant yet subtle role in shaping the dynamics of neuronal networks.In particular,regions of irregular and regular propagating excitatory fronts related to the synchronization transitions appear intermittently as the delay increases.Moreover,the fraction of working sodium and potassium ion channels can also have a significant impact on the spatiotemporal dynamics of neuronal networks.As the fraction of blocked sodium channels increases,the frequency of excitatory events decreases,which in turn manifests as an increase in the neuronal synchrony that,however,is dysfunctional due to the virtual absence of large-amplitude excitations.Expectedly,we also show that larger coupling strengths improve synchronization irrespective of the information transmission delay and channel blocking.The presented results are also robust against the variation of the network size,thus providing insights that could facilitate understanding of the joint impact of ion channel blocking and information transmission delay on the spatiotemporal dynamics of neuronal networks.     

生物神经网络系统动力学与功能研究

生物神经系统是由数量极其巨大的神经元相互联结的信息网络系统,在生物体的感觉、认知和运动控制中发挥关键性的作用.首先介绍神经元、大脑和一些生物神经网络的生理结构和理论模型,然后分别介绍其放电活动和网络动态特性的一些重要问题,包括神经元的复杂放电模式、耦合神经元网络系统的同步活动和时空动力学、大脑联合皮层神经微回路的网络结构特征,以及工作记忆和抉择过程的动力学机制等. 最后对今后研究给出一些展望.      

Projective synchronization of a class of complex network based on high-order sliding mode control

Projective synchronization of a class of complex networks is investigated using second-order sliding mode control. The sliding surface and the control input are designed based on stability theory. The Burgers system with spatiotemporal chaotic behavior in the physics domain is taken as nodes to constitute the complex network, and the Fisher–Kolmogorov system is taken as the tracking target. The artificial simulation results show that the synchronization technique is effective.     

Parameter identification and chaos synchronization for uncertain coupled map lattices

A method of chaos synchronization and parameter identification is proposed in the paper. The synchronization controller and the parameter recognizer are designed. Two coupled map lattices with different structures are taken as examples to verify the effectiveness of the method. Simulation results show that the identification variables in the parameter recognizer can substitute for the unknown parameters in both target and response systems. Then global synchronization of the two uncertain coupled map lattices can be realized after the designed controller is added.     

Chimera states and synchronization behavior in multilayer memristive neural networks

To study the effect of electromagnetic induction on the spatiotemporal dynamic behavior of neural networks, in this paper, we have mainly studied both the synchronization behavior and the evolution of chimera states (CS) in coupled neural networks. To do this, a multilayer memristive neural network was constructed by selecting the Hindmarsh–Rose neurons as the network nodes, and the effect of electromagnetic induction is introduced by using the cubic flux-controlled memristive model as synapse. For simplicity, the following coupling scheme is adopted: only the coupling connections for the neurons between different layers are considered with memristive synapses, while those neurons in each layer are still bidirectional coupled with the classical electrical synapses. It is found that, by adjusting the coupled strength of electrical synapses and the parameters of memristive synapses, the coexistence behavior of coherent and incoherent states, i.e., the CS, could appear in each layer. It is interesting that the CS are also found in inter-layer memristive synapse network. Furthermore, we have discussed the synchronization behavior in this multilayer memristive neural network, one can find when the whole multilayer network is in a synchronization state, not only the spatiotemporal consistency of the CS in each layer neural networks is observed, but also the memductance of all memristive synapses is completely synchronized. Our results suggest that the electromagnetic induction may play an important role in regulating the dynamic behavior of neural networks, and the introduction of memristive synapse into the biological neural network will provide useful clues for revealing the memory behavior of the neural system in human brain.     

Lag synchronization between discrete chaotic systems with diverse structure

A lag synchronization controller is designed in studying discrete chaotic systems with diverse structures to realize synchronization between Henon and Ikeda sys- terns. The structure of the lag synchronization controller and the error equations of state variables between discrete chaotic systems are presented based on the stability theory. The designed controller has unique structures for different chaotic systems. Lag synchro- nization between any discrete chaotic systems with diverse structures can be achieved. Simulation results show that this control method is effective and feasible.     

Finite-time synchronization control for uncertain Markov jump neural networks with input constraints

This paper is concerned with the problem of finite-time synchronization control for uncertain Markov jump neural networks in the presence of constraints on the control input amplitude. The parameter uncertainties under consideration are assumed to belong to a fixed convex polytope. By using a parameter-dependent Lyapunov functional and a simple matrix decoupling method, a sufficient condition is proposed to ensure that the considered networks are stochastically synchronized over a finite-time interval. The desired mode-independent controller parameters can be computed via solving a convex optimization problem. Finally, two chaos neural networks are employed to demonstrate the effectiveness of our proposed approach.     

Alternating chaos versus synchronized vibrations of interacting plate with beams

We study networks of coupled oscillators governed by ODEs and yielded by physically validated sets of a few PDEs governing dynamics of structural members (plate and beams), chaos and phase synchronization and contact/no-contact non-linear dynamics of structural members coupled via boundary conditions. We have detected, illustrated and discussed a few novel kinds of hybrid states of the studied plate-beam(s) contact/no-contact interactions as well as novel scenarios of transition into chaos exhibited by the interplay of continuous objects. Classical (time histories, phase portraits, Poincaré maps, FFT, Lyapunov exponents) and non-classical (2D Morlet wavelets) approaches are used while monitoring non-linear dynamics of the interacting spatial structural members. Our results include examples from structural mechanics and the studied objects are modelled by validated mechanical hypotheses and assumptions. Novel non-linear phenomena including switching to different vibration regimes and phase chaotic synchronization are illustrated and discussed.     

Cluster synchronization analysis of complex dynamical networks by input-to-state stability

Cluster synchronization is an interesting issue in complex dynamical networks with community structure. In this paper, we study cluster synchronization of complex networks with non-identical systems by input-to-state stability. Some sufficient conditions that ensure cluster synchronization of complex networks are provided. We show that the cluster synchronization is difficult to achieve if there are some links among different clusters. The analysis is then extended to the case where the outer coupling strengths are adaptive. Finally, numerical simulations are given to validate our theoretical analysis.     

Secure communication in wireless sensor networks based on chaos synchronization using adaptive sliding mode control

Due to resource constraints in wireless sensor networks and the presence of unwanted conditions in communication systems and transmission channels, the suggestion of a robust method which provides battery lifetime increment and relative security is of vital importance. This paper considers the secure communication in wireless sensor networks based on new robust adaptive finite time chaos synchronization approach in the presence of noise and uncertainty. For this purpose, the modified Chua oscillators are added to the base station and sensor nodes to generate the chaotic signals. Chaotic signals are impregnated with the noise and uncertainty. At first, we apply the modified independent component analysis to separate the noise from the chaotic signals. Then, using the adaptive finite-time sliding mode controller, a control law and an adaptive parameter-tuning method is proposed to achieve the finite-time chaos synchronization under the noisy conditions and parametric uncertainties. Synchronization between the base station and each of the sensor nodes is realized by multiplying a selection matrix by the specified chaotic signal which is broadcasted by the base station to the sensor nodes. Simulation results are presented to show the effectiveness and applicability of the proposed technique.     

Chaos control,spiral wave formation,and the emergence of spatiotemporal chaos in networked Chua circuits

In this paper, a certain kind of intermittent scheme is used to control the chaos in a single chaotic Chua circuit to reach an arbitrary orbit. Furthermore, it is confirmed to be effective in suppressing spatiotemporal chaos and a spiral wave in the networks of Chua circuits with nearest-neighbor connections. The controllable and measurable variable is sampled, and the linear error between the sampled variable and the selected thresholds is fed back into the system only if the sampled variable exceeds the thresholds; otherwise, the system will develop itself without any external perturbation. In experiments, the control scheme could be realized by using the Heavside function. In the case of one single chaotic Chua circuit, the chaotic state can be controlled to reach an arbitrary n-periodical orbit (n=1,2,3,5,6,…) with appropriate feedback intensity and thresholds. It is argued that this scheme could explain the mechanism of what is called phase compression. Then the phase compression scheme is used to control a spiral wave and spatiotemporal chaos in a network of Chua circuits with 256×256 sites. The numerical simulation results confirm its effectiveness when appropriate upper and bottom thresholds are used by monitoring the measurable output voltages of the chaotic circuit in one site of the network.     

Chaos synchronization of two different chaotic complex Chen and Lü systems

This paper investigates the phenomenon of chaos synchronization of two different chaotic complex systems of the Chen and Lü type via the methods of active control and global synchronization. In this regard, it generalizes earlier work on the synchronization of two identical oscillators in cases where the drive and response systems are different, the parameter space is larger, and the dimensionality increases due to the complexification of the dependent variables. The idea of chaos synchronization is to use the output of the drive system to control the response system so that the output of the response system converges to the output of the drive system as time increases. Lyapunov functions are derived to prove that the differences in the dynamics of the two systems converge to zero exponentially fast, explicit expressions are given for the control functions and numerical simulations are presented to illustrate the success of our chaos synchronization techniques. We also point out that the global synchronization method is better suited for synchronizing identical chaotic oscillators, as it has serious limitations when applied to the case where the drive and response systems are different.     

Convective coupled map for simulating spatiotemporal chaos in flows

A coupled map lattices with convective nonlinearity or, for short, Convective Coupled Map (CCM) is proposed in this paper to simulate spatiotemporal chaos in fluid flows. It is found that the parameter region of spatiotemporal chaos can be determined by the maximal Liapunov exponent of its complexity time series. This simple model implies a similar physical mechanism for turbulence such that the route to spatiotemporal chaos in fluid flows can be envisaged. The study is supported by “Nonlinear Sciences Project” from the State Science and Technology Commission of China.     

The complete synchronization condition in a network of piezoelectric micro-beams

This work deals with the dynamics of a network of piezoelectric micro-beams (a stack of disks). The complete synchronization condition for this class of chaotic nonlinear electromechanical system with nearest-neighbor diffusive coupling is studied. The nonlinearities within the devices studied here are in both the electrical and mechanical components. The investigation is made for the case of a large number of coupled discrete piezoelectric disks. The problem of chaos synchronization is described and converted into the analysis of the stability of the system via its differential equations. We show that the complete synchronization of N identical coupled nonlinear chaotic systems having shift invariant coupling schemes can be calculated from the synchronization of two of them. According to analytical, semi-analytical predictions and numerical calculations, the transition boundaries for chaos synchronization state in the coupled system are determined as a function of the increasing number of oscillators.