Synchronization defect lines in complex-oscillatory target waves

It is well known that one of key features of spiral waves in complex-oscillatory media is the appearance of synchronization defect lines, across which the phase of the oscillation changes by multiplies of 2π. In this Letter, we report the appearance of synchronization defect lines in target waves in complex-oscillatory media by studying a model of two-dimensional Rössler reaction-diffusion system subject to an appropriate periodic force in a small region of the center of domain. The geometric structure and stability of the defect lines are studied.     

The boundary-induced spiral wave drift in the complex Ginzburg–Landau equation

We numerically investigate the boundary-induced spiral wave drift in the complex Ginzburg–Landau equation. We find some novel phenomena for the spiral drifting dynamics such as the chaotic behaviors, the transient chaos and asymmetrical attractors.     

Wave Grouping of a Drifting Spiral Wave in the Presence of an External Field

The phenomenon of wave grouping, in which the dense waves and the sparse waves can form groups in front of the spiral tip when the spiral wave is meandering, has been reported in a chemical reaction system recently. We present a method to realize the phenomenon of wave grouping by applying an external field to the system. The numerical simulations are carried out on the basis of the FitzHugh-Nagumo equations.     

A numerical test of the collective coordinate method

The purpose of this Letter is to compare the dynamics of the kink interacting with the imperfection which follows from the collective coordinate method with the numerical results obtained on the ground of the field theoretical model. We showed that for weekly interacting kinks the collective coordinate method works similarly well for low and extremely large speeds.     

Amplified Signal Response by Neuronal Diversity on Complex Networks

The effect of diversity on dynamics of coupled FitzHugh-Nagumo neurons on complex networks is numerically investigated, where each neuron is subjected to an external subthreshold signal. With the diversity the network is a mixture of excitable and oscillatory neurons, and the diversity is determined by the variance of the system＇s parameter. The complex network is constructed by randomly adding long-range connections （shortcuts） on a nearest-neighbouring coupled one-dimensional chain. Numerical results show that external signals are maximally magnified at an intermediate value of the diversity, as in the case of well-known stochastic resonance, burthermore, the effects of the number of shortcuts and coupled strength on the diversity-induced phenomena are also discussed. These findings exhibit that the diversity may play a constructive role in response to external signal, and highlight the importance of the diversity on such complex networks.     

Phase Space Compression in One-Dimensional Complex Ginzburg-Landau Equation

The transition from stationary to oscillatory states in dynamical systems under phase space compression is investigated. By considering the model for the spatially one-dimensional complex Ginzburg-Landau equation, we find that defect turbulence can be substituted with stationary and oscillatory signals by applying system perturbation and confining variable into various ranges. The transition procedure described by the oscillatory frequency is studied via numerical simulations in detail.     

Strange Nonchaotic Attractors in a Time-Delay System

A nonchaotic attractor is observed in an infinite-dimensional system which is related to optical bistability and described by a nonlinear time-delay differential equation. The observed nonchaotic attractor is characterized by the strange trajectory of attractor but with negative value for the largest Lyapunov exponent, as well as the Fourier power spectra.     

Kinematic model of propagating arc-like segments with feedback

Using a kinematic approach, we propose a model of arc-like wave segments in which the free ends are stabilized by using a feedback algorithm. The model can demonstrate the experimental results and numerical computations of a reaction-diffusion system. This model also reveals some aspects of spiral wave dynamics with the free ends including not only the stabilization of wave segments using feedback, but also a critical behavior with respect to the initial wave size in media with fixed excitability.     

Synchronized Anti-Phase and In-Phase Oscillations of Intracellular Calcium Ions in Two Coupled Hepatocytes System

We study the dynamic behaviour of two intracellufar calcium oscillators that are coupled through gap junctions both to Ca^2＋ and inositol（1,4,5）-trisphosphate （IP3）. It is found that synchronized anti-phase and in-phase oscillations of cytoplasmic cadcium coexist in parameters space. Especially, synchronized anti-phase oscillations only occur near the onset of a Hopf bifurcation point when the velocity of IP3 synthesis is increased. In addition, two kinds of coupling effects, i.e., the diffusions of Ca^2＋ and IP3 among cells on synchronous behaviour, are considered. We fnd that small coupling of Ca^2＋ and large coupling of IP3 facilitate the emergence of synchronized anti-phase oscillations. However, the result is contrary for the synchronized in-phase case. Our findings may provide a qualitative understanding about the mechanism of synchronous behaviour of intercellular calcium signalling.     

On bifurcations in a chaotically stirred excitable medium

We study a one-dimensional filamental model of a chaotically stirred excitable medium. In a numerical simulation we systematically explore its rich bifurcation scenarios involving saddle-nodes, Hopf bifurcations and hysteresis loops. The bifurcations are described in terms of two parameters signifying the excitability of the reacting medium and the strength of the chaotic stirring, respectively. The solution behaviour, in particular at the bifurcation points, is analytically described by means of a nonperturbative variational method. Using this method we reduce the partial differential equations to either algebraic equations for stationary solutions and bifurcations, or to ordinary differential equations in the case of non-stationary solutions and bifurcations. We present numerical simulations corroborating our analytical results.     

Control of effective potential minima for Kapitza oscillator by periodical kicking pulses

Here we propose the modification of Kapitza procedure of averaging to control the effective energy minima of the oscillator driven by periodical external field. We demonstrate the effect of control with relatively low frequency of the field of oscillation to compare with sin- or cos-periodical force.     

Experimental observation of strange nonchaotic attractors in a driven excitable system

We report the observation of strange nonchaotic attractors in an electrochemical cell. The system parameters were chosen such that the system observable (anodic current) exhibits fixed point behavior or period one oscillations. These autonomous dynamics were thereafter subjected to external quasiperiodic forcing. Systematically varying the characteristics (frequency and amplitude) of the superimposed external signal; quasiperiodic, chaotic and strange nonchaotic behaviors in the anodic current were generated. The inception of strange nonchaotic attractors was verified using standard diagnostic techniques.     

Synchronization in Coupled Oscillators with Two Coexisting Attractors

Dynamics in coupled Dufling oscillators with two coexisting symmetrical attractors is investigated. For a pair of Dufl~ng oscillators coupled linearly, the transition to the synchronization generally consists of two steps： Firstly, the two oscillators have to jump onto a same attractor, then they reach synchronization similarly to coupled monostable oscillators. The transition scenarios to the synchronization observed are strongly dependent on initial conditions.     

Universality of level spacing distributions in classical chaos

We suggest that random matrix theory applied to a matrix of lengths of classical trajectories can be used in classical billiards to distinguish chaotic from non-chaotic behavior. We consider in 2D the integrable circular and rectangular billiard, the chaotic cardioid, Sinai and stadium billiard as well as mixed billiards from the Limaçon/Robnik family. From the spectrum of the length matrix we compute the level spacing distribution, the spectral auto-correlation and spectral rigidity. We observe non-generic (Dirac comb) behavior in the integrable case and Wignerian behavior in the chaotic case. For the Robnik billiard close to the circle the distribution approaches a Poissonian distribution. The length matrix elements of chaotic billiards display approximate GOE behavior. Our findings provide evidence for universality of level fluctuations—known from quantum chaos—to hold also in classical physics.     

Nonlinear adaptive synchronization rule for identification of a large amount of parameters in dynamical models

The existing adaptive synchronization technique based on the stability theory and invariance principle of dynamical systems, though theoretically proved to be valid for parameters identification in specific models, is always showing slow convergence rate and even failed in practice when the number of parameters becomes large. Here, for parameters update, a novel nonlinear adaptive rule is proposed to accelerate the rate. Its feasibility is validated by analytical arguments as well as by specific parameters identification in the Lotka-Volterra model with multiple species. Two adjustable factors in this rule influence the identification accuracy, which means that a proper choice of these factors leads to an optimal performance of this rule. In addition, a feasible method for avoiding the occurrence of the approximate linear dependence among terms with parameters on the synchronized manifold is also proposed.     

Complex network approach for recurrence analysis of time series

We propose a novel approach for analysing time series using complex network theory. We identify the recurrence matrix (calculated from time series) with the adjacency matrix of a complex network and apply measures for the characterisation of complex networks to this recurrence matrix. By using the logistic map, we illustrate the potential of these complex network measures for the detection of dynamical transitions. Finally, we apply the proposed approach to a marine palaeo-climate record and identify the subtle changes to the climate regime.     

Influence of Coloured Correlated Noises on Probability Distribution and Mean of Tumour Cell Number in the Logistic Growth Model

An approximate Fokker-Planck equation for the logistic growth model which is driven by coloured correlated noises is derived by applying the Novikov theorem and the Fox approximation. The steady-state probability distribution （SPD） and the mean of the tumour cell number are analysed. It is found that the SPD is the single extremum configuration when the degree of correlation between the multiplicative and additive noises, λ is in -1 〈λ≤0 and can be the double extrema in 0〈λ〈1. A configuration transition occurs because of the variation of noise parameters. A minimum appears in the curve of the mean of the steady-state tumour cell number, （x）, versus λ The position and the value of the minimum are controlled by the noise-correlated times.     

Taxonomy of correlations of wind velocity — an application to the Sicilian area

We present an algorithm that allows us to analyze the cross-correlation of wind velocity measured in different locations; this algorithm is applied to 29 recording stations in Sicily. The results show that such correlations present a significant and persistent ultrametric structure that is influenced by the geographical neighborhood as well as by the presence of mountain and the sea. The algorithm presented, that is also able to reveal weak correlations, can be used as a starting point for the development of multivariate models of wind.     

Breakup of Spiral Waves in Coupled Hindmarsh--Rose Neurons

Breakup of spiral wave in the Hindmarsh-Rose neurons with nearest-neighbour couplings is reported. Appropriate initial values and parameter regions are selected to develop a stable spiral wave and then the Gaussian coloured noise with different intensities and correlation times is imposed on all neurons to study the breakup of spiral wave, respectively. Based on the mean field theory, the statistical factor of synchronization is defined to analyse the evolution of spiral wave. It is found that the stable rotating spiral wave encounters breakup with increasing intensity of Gaussian coloured noise or decreasing correlation time to certain threshold.     

Warp of the Invariant Circle and Onset of Chaos in Josephson Junction Equation

The dynamics of the dc and ac driving Josephson junction equation is studied in terms of the two-dimensional Poincaré map. The smooth invariant circle on the phase cylinder in over-damped case a ） 2 loses smoothness as a decreases and becomes a strange attractor eventually. This triggers two kinds of chaos, one occurs in the regions between two Arnold tongues and the other occurs within the tongues.