Projective synchronization of the small-world delayed network with uncertainty

Spatiotemporal chaotic systems are taken as nodes to constitute the small-world delayed network with uncertainty, and projective synchronization of the network is researched. The control input of the network and the adaptive law of adjustment parameters are designed based on Lyapunov theorem. Concretely, the Burgers systems with spatiotemporal chaotic behavior in physics domain are taken as nodes to constitute the complex network, and the Fisher–Kolmogorov system is taken as the target system. The simulation results show that the synchronization performance of the network is very stable.     

Exponential stability and spectral analysis of a delayed ring neural network with a small-world connection

This paper addresses the dynamical behavior of the linearized delayed ring neural network system with a small-world connection. The semigroup approach is adopted in investigation. The asymptotic eigenvalues of the system are presented. It shows that the spectrum of the system is located in the left half complex plane and its real part goes to ??? when the connection weights between neurons are well-defined. The spectrum determined growth condition is held true and the exponential stability of the system is then established. Moreover, we present the necessary conditions for the neuron and feedback gains, for which the closed-loop system is delay-independent exponentially stable, and we further provide the sufficient and necessary conditions when the concrete number of neurons and the location of small-world connection are given. Finally, numerical simulations are presented to illustrate the convergence of the state for the system and demonstrate the effect of the feedback gain on stability.     

Chaotic burst synchronization in heterogeneous small-world neuronal network with noise

Chaotic bursting is a fundamental behavior of neurons. In this paper, global and local burst synchronization is studied in a heterogeneous small-world neuronal network of non-identical Hindmarsh-Rose (HR) neurons with noise. It is found that the network can achieve global burst synchronization much more easily than phase synchronization and nearly complete synchronization. Moreover, local burst synchronized clusters have already formed before global burst synchronization happens. We study the effect of the shortcut-adding probability and the heterogeneity coefficient on local and global burst synchronization of the network and find that the introduction of shortcuts facilitates burst synchronization while the heterogeneity has little effect. Moreover, we study the spatiotemporal pattern of the network and find that there is an optimal coupling strength range in which the periodicity of the network is very apparent.     

Dynamical analysis and control strategies of an SIVS epidemic model with imperfect vaccination on scale-free networks

Nonlinear Dynamics - Vaccination is an effective method to prevent the spread of infectious diseases. In this paper, we develop an SIVS epidemic model with degree-related transmission rates and...     

Dynamical distributed control and synchronization

Nonlinear Dynamics - It is well known that most of real-world phenomena are described by partial differential equations. Nevertheless, for control design purposes it is very common to approximate...     

Dynamical behaviors for a competition and cooperation model of enterprises with two delays

In this paper, dynamical behaviors for a competition and cooperation model of two enterprises with two delays are investigated. By choosing the diverse delay as a bifurcation parameter, we show that the complex Hopf bifurcation phenomenon at the positive equilibrium of the system can occur as the diverse delay crosses some critical values. Finally, some numerical simulations supporting our theoretical results and the economic meaning of the model are also presented.     

Time-delayed feedback control of dynamical small-world networks at Hopf bifurcation

We show that time-delayed feedback methods, which have successfully been used to control unstable steady states or periodic orbits, provide a tool to control Hopf bifurcation for a small-world network model with nonlinear interactions and time delays. We choose the interaction strength parameter as a bifurcation parameter. Without control, bifurcation will occur early; meanwhile, the model can maintain a stationary total influenced volume only in a certain domain of the interaction strength parameter. However, outside of this domain the model still possesses a stable total influenced volume that can be guaranteed by delayed feedback perturbation, and the onset of the Hopf bifurcation is postponed. The feedback perturbation vanishes if the stabilization is successful and thus the domain of stability can be extended under only small control force. We present an analytical investigation of the feedback scheme using characteristic equation and discuss effects of both a low-pass filter included in the control loop and nonzero latency times associated with generation and injection of the feedback signal.

     

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.     

Nonlinear fluctuation behaviors of complex voter financial price dynamics on small-world network

Nonlinear Dynamics - To simulate the price fluctuation dynamics of financial markets, a novel financial price model is developed by the voter dynamic system on the Watts-Strogtz small-world network...     

Dynamical behavior of a fractional three-species food chain model

Nonlinear Dynamics - In this paper, a fractional three-species food chain model is considered. The boundedness of the solution of the fractional system has been proven. We analytically determine...     

Dynamical behavior of a competition model of Telcom and Cable Television industry

Under the trend of the integration of the Internet, Telcom, and Cable Television (CATV) in China, the penetration and integration in the service of CATV industry and telecom industry will be conducted. With its service changing from the original single video transmission to the diverse communication service, the CATV industry will transform its development plan, thus the adjustment of its developmental strategies. From the influence of the involvement of the three telecommunication operators in Internet Protocol Television (IPTV) on CATV industry and the mutual competitive relationship among them, an analysis of the operating enterprises of the two industries was made by using differential equations. The results show that, under some conditions, one operator in the telecom industry will monopolize the market. And under other conditions, market share of the three operators in IPTV will change periodically.     

Bifurcation and stability analysis of a neural network model with distributed delays

In this paper, the dynamics of a generalized two-neuron model with self-connections and distributed delays are investigated, together with the stability of the equilibrium. In particular, the conditions under which the Hopf bifurcation occurs at the equilibrium are obtained for the weak kernel. This means that a family of periodic solutions bifurcates from the equilibrium when the bifurcation parameter exceeds a critical value. Explicit algorithms for determining the stability of the bifurcating periodic solutions and the direction of the Hopf bifurcation are derived by using the theory of normal form and center manifold [20]. Some numerical simulations are given to illustrate the effectiveness of the results found. The obtained results are new and they complement previously known results.This work was supported by the National Natural Science Foundation of China under Grants 60574043 and 60373067, the Natural Science Foundation of Jiangsu Province, China under Grants BK2003053.     

Dynamical analysis and anti-oscillation-based adaptive control of the FO arch MEMS with optimality

Nonlinear Dynamics - This paper mainly investigates dynamical analysis and anti-oscillation-based adaptive control issues of the fractional-order (FO) arch microelectromechanical system (MEMS) with...     

Dynamical analysis of an improved FitzHugh-Nagumo neuron model with multiplier-free implementation

The cubic-polynomial nonlinearity with N-shaped curve plays a crucial role in generating abundant electrical activities for the original FitzHugh-Nagumo (FHN) neuron model. The pioneer FHN neuron model is efficient in theoretical analysis and numerical simulation for these abundant electrical activities, but analog multipliers are indispensable in hardware implementation since the involvement of cubic-polynomial nonlinearity. Analog multiplier goes against the circuit integration of FHN neuron model due to its huge implementation costs. To avoid the involvement of analog multiplier in hardware implementation, a nonlinear function possessing N-shaped curve and multiplier-free implementation is presented in this paper. To confirm the availability of this nonlinear function in generating electrical activities, numerical simulations and hardware experiments are successfully executed on an improved two-dimensional (2D) FHN neuron model with externally applied stimulus. The results demonstrate that the improved FHN neuron model can generate rich electrical activities of periodic spiking behavior, chaotic behavior, and quasi-periodic behavior. Analog circuit implementation without any multiplier and its hardware experiment show the availability of the proposed nonlinear function, which is appropriate for analog circuit implementation of FHN neuron-based neuromorphic intelligence.

     

Firing synchronization of learning neuronal networks with small-world connectivity

The properties of firing synchronization of learning neuronal networks, electrically and chemically coupled ones, with small-world connectivity are studied. First, the variation properties of synaptic weights are examined. Next the effects of the synaptic learning rate on the properties of firing rate and synchronization are investigated. The influences of the coupling strength and the shortcut probability on synchronization are also explored. It is shown that synaptic learning suppresses over-excitement for the networks, helps synchronization for the electrically coupled neuronal network but destroys synchronization for the chemically coupled one. Both introducing shortcuts and increasing the coupling strength are helpful in improving synchronization of the neuronal networks. The spatio-temporal patterns illustrate and confirm the above results.