Chaos quasisynchronization induced by impulses with parameter mismatches

This paper studies the effect of parameter mismatch on the impulsive synchronization of a class of coupled chaotic systems. A new definition for global quasisynchronization is introduced and used to analyze the synchronous behavior of coupled chaotic systems in the presence of parameter mismatch. Using the linear decomposition and comparison-system methods, a global synchronization error bound together with a sufficient condition is derived. Numerical simulations on the chaotic Chua's circuit are presented to verify the theoretical results.     

Analysis and circuit realization of intermittency with multiple laminar states

In this Letter, an electrical circuit is built for realizing the multi-state intermittency generated by a simple force-driven chaotic system. The intermittency phenomenon and its underlaying mechanism are analyzed, and the experimental results are discussed. It is shown that, with two classes of invariant subspaces, the number of the laminar states and the distance between the adjacent laminar states of the created multi-state on-off intermittency can be arbitrarily changed by manipulating the control parameters.     

Pinning control of scale-free dynamical networks

Recently, it has been demonstrated that many large complex networks display a scale-free feature, that is, their connectivity distributions have the power-law form. In the present work, control of a scale-free dynamical network by applying local feedback injections to a fraction of network nodes is investigated. The specifically and randomly pinning schemes are considered. The specifically pinning of the most highly connected nodes is shown to require a significantly smaller number of local controllers as compared to the randomly pinning scheme. The method is applied to an array of Chua's oscillators as an example.     

Synchronization of hyperchaotic oscillators via single unidirectional chaotic-coupling

In this paper, synchronization of two hyperchaotic oscillators via a single variable’s unidirectional coupling is studied. First, the synchronizability of the coupled hyperchaotic oscillators is proved mathematically. Then, the convergence speed of this synchronization scheme is analyzed. In order to speed up the response with a relatively large coupling strength, two kinds of chaotic coupling synchronization schemes are proposed. In terms of numerical simulations and the numerical calculation of the largest conditional Lyapunov exponent, it is shown that in a given range of coupling strengths, chaotic-coupling synchronization is quicker than the typical continuous-coupling synchronization. Furthermore, A circuit realization based on the chaotic synchronization scheme is designed and Pspice circuit simulation validates the simulated hyperchaos synchronization mechanism.     

Equivalent linear observer-based tracker for stochastic chaotic system with delays and disturbances

Based on the state-space self-tuning control methodology, aunified method for determining the equivalent linear observer-basedtracker for a stochastic chaotic system with input and statedelays and deterministic disturbances is developed. In thisapproach, an equivalent linear observer is obtained for theconcerned complex system, which may have unknown system parameters,system and measurement noises, and inaccessible system states.More precisely, an equivalent delay-free system is obtainedin the estimating process of the self-tuning control loop, andthen a linear controller and an observer are designed. The proposedmethod significantly simplifies the design and the implementationprocedures of the tracker.     

Detecting the topologies of complex networks with stochastic perturbations

How to recover the underlying connection topology of a complex network from observed time series of a component variable of each node subject to random perturbations is studied. A new technique termed Piecewise Granger Causality is proposed. The validity of the new approach is illustrated with two FitzHugh-Nagumo neurobiological networks by only observing the membrane potential of each neuron, where the neurons are coupled linearly and nonlinearly, respectively. Comparison with the traditional Granger causality test is performed, and it is found that the new approach outperforms the traditional one. The impact of the network coupling strength and the noise intensity, as well as the data length of each partition of the time series, is further analyzed in detail. Finally, an application to a network composed of coupled chaotic Ro?ssler systems is provided for further validation of the new method.     

Mean first-passage time for random walks on undirected networks

In this paper, by using two different techniques we derive an explicit formula for the mean first-passage time (MFPT) between any pair of nodes on a general undirected network, which is expressed in terms of eigenvalues and eigenvectors of an associated matrix similar to the transition matrix. We then apply the formula to derive a lower bound for the MFPT to arrive at a given node with the starting point chosen from the stationary distribution over the set of nodes. We show that for a correlated scale-free network of size N with a degree distribution P(d) ∼ d ^−γ , the scaling of the lower bound is N ^1−1/γ . Also, we provide a simple derivation for an eigentime identity. Our work leads to a comprehensive understanding of recent results about random walks on complex networks, especially on scale-free networks.     

Precursor criteria for noise-induced critical transitions in multi-stable systems

Nonlinear Dynamics - Predicting noise-induced critical transitions between multi-stable states of a dynamical system is of uttermost importance in various fields. This paper investigates a...     

A new hyperchaotic system and its circuit implementation

A new hyperchaotic system which has two large positive Lyapunov exponents is presented and physically implemented. Spectral analysis shows that the system in the hyperchaotic mode has an extremely broad frequency bandwidth of high magnitudes, verifying its unusual random nature and indicating its great potential for some relevant engineering applications such as secure communications.