Annihilation and creation of rotating waves by a local light pulse in a protoplasmic droplet of the Physarum plasmodium

Pattern dynamics plays a fundamental role in biological functions from cell to organ in living systems, and the appearance of rotating waves can lead to pathological situations. Basic dynamics of rotating waves of contraction-relaxation activity under local perturbation is studied in a newly developed protoplasmic droplet of the Physarum plasmodium. A light pulse is applied by irradiating circularly a quarter of the droplet showing a single rotating wave. The oscillation pattern changes abruptly only when the irradiation is applied at a part of the droplet near the maximal contraction. The abrupt changes are as follows: the rotating wave disappears or is displaced when the irradiation area is very close to the center of the rotating wave, while new rotating waves are created when the irradiation area is far from the center of the rotating wave. These results support the hypothesis that the phase response curve has a discontinuous change (type 0 resetting) from delay to advance around the maximal contraction. The significance of the results is discussed in relation to “vulnerability” in excitable media and biological systems in general.     

Size transition of spiral waves using the pulse array method

The domain size of spiral waves is an important issue in studies of two-dimensional (2D) spatiotemporal patterns. In this work, we use the 2D complex Ginzburg--Landau equation (CGLE) as our model and find that an initially big spiral can successfully transfer to several small spirals by applying a pulse array method. The impacts of several important factors, such as array density, controlling intensity and pulsing time, are investigated. This control approach may be useful for the control of 2D spatiotemporal patterns and has potential applications in the control of some realistic systems, such as meteorological and cardiac systems.     

复Ginzburg-Landau方程中模螺旋波的稳定性研究

研究了复Ginzburg-Landau方程系统中模螺旋波与其他斑图在同一平面内的竞争行为,发现演化结果在系统参数平面内可分为四个主要区域:在I区和III区中,模螺旋波与相螺旋波相比稳定性较差,模螺旋波的空间被相螺旋波所入侵.在II区中,模螺旋波具有较强的稳定性,相螺旋波的空间被模螺旋波所入侵.在IV区内,由于时空混沌所导致的频率不稳定性,演化的结果较为复杂.我们通过对模螺旋波、相螺旋波以及时空混沌的频率分析,发现当模螺旋波的系统参数为α1=-1.34,β1=0.35时,较高频率的模螺旋波具有较好的稳定性,高频模螺旋波可以入侵低频斑图空间.竞争结果主要受系统变量实部的频率影响,频率分析所得到的理论结果与数值实验结果符合得非常好.     

Synchronization and propagation of bursts in networks of coupled map neurons

The present paper studies regular and complex spatiotemporal behaviors in networks of coupled map-based bursting oscillators. In-phase and antiphase synchronization of bursts are studied, explaining their underlying mechanisms in order to determine how network parameters separate them. Conditions for emergent bursting in the coupled system are derived from our analysis. In the region of emergence, patterns of chaotic transitions between synchronization and propagation of bursts are found. We show that they consist of transient standing and rotating waves induced by symmetry-breaking bifurcations, and can be viewed as a manifestation of the phenomenon of chaotic itinerancy.     

Oscillations and Waves in a Nonlinear System with the 1/<Emphasis Type="Italic">f</Emphasis> Spectrum

Numerical methods are used to study a spatially distributed system of two nonlinear stochastic equations that simulate interacting phase transitions. Conditions for self-oscillations and waves are determined. The 1/f and 1/k spectra of extreme fluctuations are formed when waves emerge and move under the action of white noise. The distribution of the extreme fluctuations corresponds to the maximum entropy, which is proven by the stability of the 1/f and 1/k spectra. The formation and motion of waves under external periodic perturbation are accompanied by spatiotemporal chaotic resonance in which the domain of periodic pulsations is extended under the action of white noise.     

Segmented waves from a spatiotemporal transverse wave instability

We observe traveling waves emitted from Turing spots in the chlorine dioxide-iodine-malonic acid reaction. The newborn waves are continuous, but they break into segments as they propagate, and the propagation of these segments ultimately gives rise to spatiotemporal chaos. We model the wave-breaking process and the motion of the chaotic segments. We find stable segmented spirals as well. We attribute the segmentation to an interaction between front rippling via a transverse instability and front symmetry breaking by a fast-diffusing inhibitor far from the codimension-2 Hopf-Turing bifurcation, and the chaos to a secondary instability of the periodic segmentation.     

Dynamical study and control of drift waves in a magnetized laboratory plasma

The various dynamical regimes of collisional drift waves in a magnetized plasma column are experimentally studied. These unstable low-frequency electrostatic waves are related with strong modulations of the ion and electron density. The angular velocity of the rotating plasma column is the control parameter of the dynamics: regular, chaotic and turbulent regimes are obtained. The spatial extension of the system allows for the occurrence of spatiotemporal chaos. The time-delay auto-synchronization method of controlling chaos [K. Pyragas, Phys. Lett. A 170, 421 (1992)] though purely temporal is successfully applied. A numerical study using coupled nonlinear oscillators exhibiting chaos is compared to the experimental results. The control method is tested on this model.     

Pursuit-evasion predator-prey waves in two spatial dimensions

We consider a spatially distributed population dynamics model with excitable predator-prey kinetics, where species propagate in space due to their taxis with respect to each other's gradient in addition to, or instead of, their diffusive spread. Earlier, we have described new phenomena in this model in one spatial dimension, not found in analogous systems without taxis: reflecting and self-splitting waves. Here we identify new phenomena in two spatial dimensions: unusual patterns of meander of spirals, partial reflection of waves, swelling wave tips, attachment of free wave ends to wave backs, and as a result, a novel mechanism of self-supporting complicated spatiotemporal activity, unknown in reaction-diffusion population models.     

Complex patterns in reactive microemulsions: self-organized nanostructures?

In a reverse microemulsion consisting of water, oil (octane), an anionic surfactant [aerosol OT (AOT)], and the reactants of the oscillating Belousov-Zhabotinsky (BZ) reaction, a variety of complex spatiotemporal patterns appear. These include traveling and standing waves, spirals that move either toward or away from their centers, spatiotemporal chaos, Turing patterns, segmented waves, and localized structures, both stationary and oscillatory. The system consists of nanometer-sized droplets of water containing the BZ reactants surrounded by a monolayer of AOT, swimming in a sea of oil, through which nonpolar BZ intermediates can diffuse rapidly. We present experimental and computational results on this fascinating system and comment on possible future directions for research.     

Emergence of spatiotemporal chaos arising from far-field breakup of spiral waves in the plankton ecological systems

It has been reported that the minimal spatially extended phytoplankton--zooplankton system exhibits both temporal regular/chaotic behaviour, and spatiotemporal chaos in a patchy environment. As a further investigation by means of computer simulations and theoretical analysis, in this paper we observe that the spiral waves may exist and the spatiotemporal chaos emerge when the parameters are within the mixed Turing--Hopf bifurcation region, which arises from the far-field breakup of the spiral waves over a large range of diffusion coefficients of phytoplankton and zooplankton. Moreover, the spatiotemporal chaos arising from the far-field breakup of spiral waves does not gradually invade the whole space of that region. Our results are confirmed by nonlinear bifurcation of wave trains. We also discuss ecological implications of these spatially structured patterns.     

If BZ medium did spanning trees these would be the same trees as Physarum built

A sub-excitable Belousov-Zhabotinsky (BZ) medium exhibits self-localized wave-fragments which may travel for relatively long time preserving their shape. Using Oregonator model of the BZ medium we imitate foraging behavior of a true slime mold, Physarum polycephalum, on a nutrient-poor substrate. We show that given erosion post-processing operations the BZ medium can approximate a spanning tree of a planar set and thus is computationally equivalent to Physarum in the domain of proximity graph construction.     

Solitary wave interactions in lattice systems with pure higher-order nonlinearity

In this paper, we investigate in detail the interactions of solitary waves in lattice systems with interaction potential V(q)=qⁿ/n, where n is 4,6,8…, through their all possible collision types, and establish a quantitative connection between the scattering property of solitary waves and the chaotic dynamics of the systems. Kink and antikink are excited in such lattice systems and the variation of their scattering effect with n is concerned. After a kink-antikink collision, the dominant interaction in the systems, if n is small, is that solitary waves pass through each other and the scattering effect increases with n; if n is large, solitary waves reflect back sometimes due to the influence of phase and this leads to a decrease of the scattering effect with n. The largest Lyapunov exponents of systems at fixed energy density first increase and then decrease with n, which is consistent with a variation of the scattering effect. The application of the special scattering behaviors between kink and antikink in information propagation is also discussed.     

Spatiotemporal chaos synchronization of an uncertain network based on sliding mode control

The sliding mode control method is used to study spatiotemporal chaos synchronization of an uncertain network.The method is extended from synchronization between two chaotic systems to the synchronization of complex network composed of N spatiotemporal chaotic systems.The sliding surface of the network and the control input are designed.Furthermore,the effectiveness of the method is analysed based on the stability theory.The Burgers equation with spatiotemporal chaos behavior is taken as an example to simulate the experiment.It is found that the synchronization performance of the network is very stable.     

Synchronization of spatiotemporal semiconductor lasers and its application in color image encryption

Optical chaos is a topic of current research characterized by high-dimensional nonlinearity which is attributed to the delay-induced dynamics, high bandwidth and easy modular implementation of optical feedback. In light of these facts, which add enough confusion and diffusion properties for secure communications, we explore the synchronization phenomena in spatiotemporal semiconductor laser systems. The novel system is used in a two-phase colored image encryption process. The high-dimensional chaotic attractor generated by the system produces a completely randomized chaotic time series, which is ideal in the secure encoding of messages. The scheme thus illustrated is a two-phase encryption method, which provides sufficiently high confusion and diffusion properties of chaotic cryptosystem employed with unique data sets of processed chaotic sequences. In this novel method of cryptography, the chaotic phase masks are represented as images using the chaotic sequences as the elements of the image. The scheme drastically permutes the positions of the picture elements. The next additional layer of security further alters the statistical information of the original image to a great extent along the three-color planes. The intermediate results during encryption demonstrate the infeasibility for an unauthorized user to decipher the cipher image. Exhaustive statistical tests conducted validate that the scheme is robust against noise and resistant to common attacks due to the double shield of encryption and the infinite dimensionality of the relevant system of partial differential equations.     

Dynamics of a neural network model with finite connectivity and cycle stored patterns

The spatiotemporal evolution and memory retrieval properties of a Hopfield-like neural network with cycle-stored patterns and finite connectivity are studied. The analytical studies on a mean-field version show that, given the number of stored patterns p, there is a critical connectivity k_c such that the retrieval states are stable fixed points if and only if k > k_c. The dependence of k_c on the number of stored patterns is also present. The numerical simulations are applied to the short-ranged model with local interaction. It is revealed that, given p, the memory retrieval function is kept if the connectivity is high enough while the dynamics of the system is in the frozen phase. However when the connectivity k is less than a critical value k_c the system is in the chaotic phase and loses its memory retrieval ability. The critical points of both the dynamical phase transition and memory-loss phase transition are obtained by simulation data.     

Exponential transient rotating waves in a bistable ring of unidirectionally coupled maps

Properties of transient rotating waves in a bistable ring of unidirectionally coupled antisymmetric cubic maps are studied. A kinematical model shows that the duration of rotating waves increases exponentially with the number of elements. The probability density function of the duration of rotating waves generated under random initial conditions has a power law form up to a cut-off. In addition, spatiotemporal noise of intermediate intensity makes the duration of rotating waves increase. Further, rotating waves are stabilized through bifurcations of steady states as coupling strength increases.     

Understanding the sub-critical transition to turbulence in wall flows

In contrast with free shear flows presenting velocity profiles with inflection points which cascade to turbulence in a relatively mild way, wall bounded flows are deprived of (inertial) instability modes at low Reynolds numbers and become turbulent in a much wilder way, most often marked by the coexistence of laminar and turbulent domains at intermediate Reynolds numbers, well below the range where (viscous) instabilities can show up. There can even be no unstable mode at all, as for plane Couette flow (pCf) or for Poiseuille pipe flow (Ppf) that are currently the subject of intense research. Though the mechanisms involved in the transition to turbulence in wall flows are now better understood, statistical properties of the transition itself are yet unsatisfactorily assessed. A widely accepted interpretation rests on non-trivial solutions of the Navier-Stokes equations in the form of unstable travelling waves and on transient chaotic states associated to chaotic repellors. Whether these concepts typical of the theory of temporal chaos are really appropriate is yet unclear owing to the fact that, strictly speaking, they apply when confinement in physical space is effective while the physical systems considered are rather extended in at least one space direction, so that spatiotemporal behaviour cannot be ruled out in the transitional regime. The case of pCf will be examined in this perspective through numerical simulations of a model with reduced cross-stream (y) dependence, focusing on the in-plane (x, z) space dependence of a few velocity amplitudes. In the large aspect-ratio limit, the transition to turbulence takes place via spatiotemporal intermittency and we shall attempt to make a connection with the theory of first-order (thermodynamic) phase transitions, as suggested long ago by Pomeau.      

A new traveling wave phenomenon of Dictyostelium in the presence of cAMP

The emergence of wave patterns in chemical and biological systems is of interest for the understanding of development, differentiation, signaling, and other phenomena. In this work we report a new type of wave pattern - called the “global wave” - which was observed in populations of Dictyostelium discoideum cells exposed to an excess of cyclic adenosine- 3′, 5′- monophosphate (cAMP) added to the supporting agar. It has been found that the addition of different amounts of cAMP to the agar leads to important deviations from the standard course of aggregation: (i) the formation and propagation of a global wave that has not been observed before; (ii) the delayed onset or absence of cAMP waves patterning; (iii) an atypical mechanism of cells clustering; and (iv) a faster or incomplete developmental cycle. We suggest that the global wave is a chemotactic response of the Dictyostelium cells to a wave of the cAMP concentration.     

Synchronization of spatiotemporal chaos in a class of complex dynamical networks

This paper studies the synchronization of complex dynamical networks constructed by spatiotemporal chaotic systems with unknown parameters. The state variables in the systems with uncertain parameters are used to construct the parameter recognizers, and the unknown parameters are identified. Uncertain spatiotemporal chaotic systems are taken as the nodes of complex dynamical networks, connection among the nodes of all the spatiotemporal chaotic systems is of nonlinear coupling. The structure of the coupling functions between the connected nodes and the control gain are obtained based on Lyapunov stability theory. It is seen that stable chaos synchronization exists in the whole network when the control gain is in a certain range. The Gray--Scott models which have spatiotemporal chaotic behaviour are taken as examples for simulation and the results show that the method is very effective.     

Asynchronous updating of threshold-coupled chaotic neurons

We study a network of chaotic model neurons incorporating threshold-activated coupling. We obtain a wide range of spatiotemporal patterns under varying degrees of asynchronicity in the evolution of the neuronal components. For instance, we find that sequential updating of threshold-coupled chaotic neurons can yield dynamical switching of the individual neurons between two states. So varying the asynchronicity in the updating scheme can serve as a control mechanism to extract different responses, and this can have possible applications in computation and information processing.