2,312 publications from this institution
We study random walks on a family of treelike regular fractals with a trap fixed on a central node. We obtain all the eigenvalues and their corresponding multiplicities for the associated stochastic master equation, with the eigenvalues being provided through an explicit recursive relation. We also evaluate the smallest eigenvalue and show that its reciprocal is approximately equal to the mean trapping time. We expect that our technique can also be adapted to other regular fractals with treelike structures.
The pinning control strategy, including specifically pinning scheme and randomly pinning scheme, is used to stabilize scale-free networks in this paper. A scale-free dynamical network model is first introduced and then, based on this model, a stability condition is derived in terms of a linear matrix inequality. Finally, a numerical simulation example is provided to verify the theoretical results.
The notion of small-world networks, recently introduced by Watts and Strogatz, has attracted increasing interest in studying the interesting properties of complex networks. Notice that, a signal or influence travelling on a small-world network often is associated with time-delay features, which are very common in biological and physical networks. Also, the interactions within nodes in a small-world network are often nonlinear. In this paper, we consider a small-world networks model with nonlinear interactions and time delays, which was recently considered by Yang. By choosing the nonlinear interaction strength as a bifurcation parameter, we prove that Hopf bifurcation occurs. We determine the stability of the bifurcating periodic solutions and the direction of the Hopf bifurcation by applying the normal form theory and the center manifold theorem. Finally, we show a numerical example to verify the theoretical analysis.
In the past few years, the discovery of small-world and scale-free properties of many natural and artificial complex networks has stimulated a great deal of interest in studying the underlying organizing principles of various complex networks, which has led to dramatic advances in this emerging and active field of research. The present article reviews some basic concepts, important progress, and significant results in the current studies of various complex networks, with emphasis on the relationship between the topology and the dynamics of such complex networks. Some fundamental properties and typical complex network models are described; and, as an example, epidemic dynamics are analyzed and discussed in some detail. Finally, the important issue of robustness versus fragility of dynamical synchronization in complex networks is introduced and discussed.
This paper discusses impulsive effects on fractional differential equations. Two approaches are taken to obtain our results: either with fixed or changing lower limits in Caputo fractional derivatives. First, we derive an existence result for periodic solutions of fractional differential equations with periodically changing lower limits. Then, the impulsive effects are modeled for fractional differential equations regarding the nonlinearities rather than the initial value conditions. The proposed impulsive model differs from common discontinuous and nonsmooth dynamical systems.
In this paper, it is proved that, for the truth value algebra of interval-valued fuzzy sets, the distributive laws do not imply the monotonicity condition for the set inclusion operation. Then, a lattice-ordered $t_{r}$-norm, which is not the convolution of $t$-norms on $[0, 1]$, is obtained. These results negatively answer two open problems posed by Walker and Walker in [15].
Implementing compact and energy-efficient synaptic elements using nanoscale memristors has elicited widespread interest in building neural network circuits. Not only can the memristive neural network offer powerful computation capability, but it also exhibits intelligent behaviors such as cognition and associative memory. In this paper, a memristor-based associative memory neural network (m-ASNN) with properties of associative memory and memory losing is designed and further used to reflect some human affections in social relationships. Specifically, a voltage-controlled memristor model with a programming threshold and forgetting property is proposed and employed as the 1M (memristor) electronic synapse. Such a memristor synapse can learn and store information, and is plastic to the activities of its presynaptic and postsynaptic neurons, like biological synapses. Furthermore, an M-ASNN consisting of the memristor synapse as well as inhibitory and excitatory neurons is built to model the forming, keeping and losing of some affections in social relationships. Finally, an analog implementation of the M-ASNN based on PSPICE is presented and simulated. The novel modeling and implementation of human affections using memristor devices may create new opportunities for affection computing as well as applications of memristive neural networks.
This article addresses the global synchronisation problem of a network of coupled Lur'e systems from the perspective of global synchronised region. A decomposition approach is proposed to convert the synchronisation of high-dimensional Lur'e networks into the test of a set of matrix inequalities whose dimensions are the same as a single Lur'e node. The notion of global synchronised region is then introduced and analysed. A necessary and sufficient condition is derived for the existence of the inner-linking matrix to guarantee a desirable unbounded synchronised region. A multi-step design procedure is given for constructing such an inner-linking matrix, which maintains a favourable decoupling property. Furthermore, the global H ∞ synchronised region is characterised for evaluating the performance of a Lur'e network subject to external disturbances. The effectiveness of the theoretical results is demonstrated through a network of Chua's circuits. Keywords: global synchronisationcomplex networkLur'e systemsynchronised region H ∞ control Acknowledgement This work was supported by the Natural Science Foundation of China under Grant Nos. 60974078, 10832006, and by China Postdoctoral Science Foundation.
Synchronization of randomly coupled networks, with each node being a van der Pol oscillator subject to parametric excitation, is studied in the present paper. The effects of the network structure, the initial conditions and the intensity of Gaussian white noise on the synchronization performance of diffusively coupled oscillators are also investigated. It is found that unidirectionally coupled dynamical networks with proper parametric excitation can achieve synchronization, and it is interesting to reveal that stochastic excitation can even accelerate network synchronization under certain initial conditions and initial intensity of stochastic excitation.
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