时空调制对可激发介质螺旋波波头动力学行为影响及控制研究

本文首先研究了时空调制对可激发介质中周期螺旋波波头动力学行为的影响. 随着时空调制的增大, 螺旋波经历了周期螺旋波、外滚螺旋波、旅行螺旋波和内滚螺旋波的显著变化. 通过定义序参量来定量的描述由时空调制引起的螺旋波在不同态之间非平衡跃迁的临界条件, 及漫游螺旋波波头圆滚圆半径随调制参数的变化情况. 当时空调制增大到某个临界值时, 螺旋波发生了破碎; 再增加时空调制, 螺旋波则发生了衰减, 系统最终演化为空间均匀静息态. 在文中给出了螺旋波发生破碎和衰减的机理和原因. 最后将时空调制方法运用于漫游螺旋波, 实现了将漫游螺旋波控制成周期螺旋波, 或将其控制为空间均匀静息态.     

Phase ordering induced by defects in chaotic bistable media

The phase ordering dynamics of coupled chaotic bistable maps on lattices with defects is investigated. The statistical properties of the system are characterized by means of the average normalized size of spatial domains of equivalent spin variables that define the phases. It is found that spatial defects can induce the formation of domains in bistable spatiotemporal systems. The minimum distance between defects acts as parameter for a transition from a homogeneous state to a heterogeneous regime where two phases coexist The critical exponent of this transition also exhibits a transition when the coupling is increased, indicating the presence of a new class of domain where both phases coexist forming a chessboard pattern.     

Regular and Chaotic Spatiotemporal Patterns in a Model of Slime Mold Aggregation

In this paper we proposed a spatial modulated two-variable Martiel-Goldbeter model to describe the complex spatiotemporal disorder dynamical behavior during development of Dictyostelium discoideum strain FR17. As the nonlinear modulated parameter A and diffusion coefficient E varied, the system shows: 1) multiperiodic phase, 2) co-existence phase of chaotic and multi-periodic state, 3) spatiotemporal chaotic phase, 4) co-existence phase of chaotic, multi-periodic and steady state, and 5) co-existence phase of chaotic and steady state. These phases can be described by spatiotemporal power spectra, pattern distribution function and Lyapunov spectra. We believed that the complex spatiotemporal disorder dynamical behavior during development of Dictyosteliurn discoideum strain FR17 is a spatiotemporal chaotic state.     

Collapse of spatiotemporal chaos

The transient nature of spatiotemporal chaos is examined in reaction-diffusion systems with coexisting stable states. We find the apparent asymptotic spatiotemporal chaos of the Gray-Scott system to be transient, with the average transient lifetime increasing exponentially with medium size. The collapse of spatiotemporal chaos arises when statistical spatial correlations produce a quasihomogeneous medium, and the system obeys its zero-dimensional dynamics to relax to its stable asymptotic state.     

终端含NMOS反相器传输线系统中的时空复杂行为分析

应用行波理论,建立了一个终端含N沟道金属氧化物半导体(N-channel metal oxide semiconductor, NMOS)反相器的传输线系统的非线性离散映射模型.对该模型进行仿真发现, 反射系数的变化可能导致系统出现时空分岔和时空混沌等复杂的时空行为, 并且初始分布对系统达到稳态后的时空行为有很大影响,零初始分布对应的时空图样比较规则, 而非零的初值分布则会导致沿线电压出现复杂的时空图样,分析表明这些时空复杂行为的产生 源于系统中传输线的无穷维本质和NMOS反相器的非线性伏安特性.     

Specific external forcing of spatiotemporal dynamics in reaction-diffusion systems

Self-organization behavior and in particular pattern forming spatiotemporal dynamics play an important role in far from equilibrium chemical and biochemical systems. Specific external forcing and control of self-organizing processes might be of great benefit in various applications ranging from technical systems to modern biomedical research. We demonstrate that in a cellular chemotaxis system modeled by one-dimensional reaction-diffusion equations particular forms of spatiotemporal dynamics can be induced and stabilized by controlling spatially distributed influx patterns of a chemical species as a function of time. In our model study we show that a propagating wave with certain shape and velocity and static symmetrical and asymmetrical patterns can be forced and manipulated by numerically computing open-loop optimal influx controls.     

一种时延范德波尔电磁系统中的复杂行为(Ⅱ)——时空混沌图案动态

对于一个由线性无损传输线加非线性边界条件组成的简单无穷维电磁系统，应用行波理论确定了电压反射波的局部映射关系.数值仿真结果表明，当系统参数发生变化时，传输线沿线电压存在着非常丰富的时空非线性现象.通过描绘出空间振幅变化图和时空行为发展图，定性分析了传输线沿线电压的时空混沌图案动态，为研究和理解时空混沌提供了一种良好的可求解模型. 关键词： 图案 时空混沌 无穷维系统 时延范德波尔电磁系统     

Chaotic transients in spatially extended systems

Different transient-chaos related phenomena of spatiotemporal systems are reviewed. Special attention is paid to cases where spatiotemporal chaos appears in the form of chaotic transients only. The asymptotic state is then spatially regular. In systems of completely different origins, ranging from fluid dynamics to chemistry and biology, the average lifetimes of these spatiotemporal transients are found, however, to grow rapidly with the system size, often in an exponential fashion. For sufficiently large spatial extension, the lifetime might turn out to be larger than any physically realizable time. There is increasing numerical and experimental evidence that in many systems such transients mask the real attractors. Attractors may then not be relevant to certain types of spatiotemporal chaos, or turbulence. The observable dynamics is governed typically by a high-dimensional chaotic saddle. We review the origin of exponential scaling of the transient lifetime with the system size, and compare this with a similar scaling with system parameters known in low-dimensional problems. The effect of weak noise on such supertransients is discussed. Different crisis phenomena of spatiotemporal systems are presented and fractal properties of the chaotic saddles underlying high-dimensional supertransients are discussed. The recent discovery according to which turbulence in pipe flows is a very long lasting transient sheds new light on chaotic transients in other spatially extended systems.     

Spinning-top dynamics of photorefractive grating

The photorefractive grating generated by two coupled waves produces a rich spatiotemporal dynamics such as those of solitons and chaos. In this paper, the dynamics of grating along with the slow-varying envelope of two coupled waves is studied where the photorefractive-coupling constant is large or more importantly the dynamics is much faster than the photorefractive response time of the material. Under this condition, new solutions of the dynamic grating equations are presented and analytically solved in the form of the Jacobi’s Elliptic functions. The spatiotemporal grating can result in a periodic space-charge field which in turn generates the space charge waves in the periodic case as a result of the spatiotemporal dynamics of the anisotropic two-wave mixing process. The theoretical work of the limiting case is in good agreement with the experimental results using a BaTiO₃ crystal.     

水平流作用下行波对流的成长及周期性重复

数值模拟研究了在极其微弱的水平流动作用下，混合流体Rayleigh-Benard对流系统一 维行波斑图的成长及其时空演化问题.揭示了系统行波对流的周期性现象及其对水平流动强 度的依赖性. 关键词： 时空斑图 混合流体对流 水平流     

Chaotic behavior in transverse-mode laser dynamics

We analyze chaotic behavior found in numerical simulations of the transverse pattern dynamics of a laser demonstrating that in some cases chaos originates in phase dynamics and is of low dimension. Investigations of both a Ginzburg-Landau equation for the complex field amplitude of the laser output and a Kuramoto-Sivashinsky-type equation for only the phase of that complex field equation find the same behavior. Both equations can be expanded in terms of spatial modes and in the chaotic regime the behavior of the modal amplitudes seems relatively independent. However, the fluctuations of the modal amplitudes are sufficiently correlated so that the spatiotemporal dynamics is a form of low dimensional chaos rather than a more complex turbulent behavior or even one that might merit the term spatiotemporal chaos.     

Real-time nonlinear feedback control of pattern formation in (bio)chemical reaction-diffusion processes: a model study

Theoretical and experimental studies related to manipulation of pattern formation in self-organizing reaction-diffusion processes by appropriate control stimuli become increasingly important both in chemical engineering and cellular biochemistry. In a model study, we demonstrate here exemplarily the application of an efficient nonlinear model predictive control (NMPC) algorithm to real-time optimal feedback control of pattern formation in a bacterial chemotaxis system modeled by nonlinear partial differential equations. The corresponding drift-diffusion model type is representative for many (bio)chemical systems involving nonlinear reaction dynamics and nonlinear diffusion. We show how the computed optimal feedback control strategy exploits the system inherent physical property of wave propagation to achieve desired control aims. We discuss various applications of our approach to optimal control of spatiotemporal dynamics.     

Excitable Structures in Stochastic Bistable Media

We examine the influence of parametric noise on the spatiotemporal behavior of a bistable medium with activator–inhibitor dynamics. Deterministic front propagation in one dimension is seen to be destabilized by the external noise, resulting in the propagation of solitary pulses through the system. For large enough noise levels, this state becomes unstable via a backfiring mechanism, which eventually leads to a turbulent state.     

Mutual adaptation of a Faraday instability pattern with its flexible boundaries in floating fluid drops

Hydrodynamic instabilities are usually investigated in confined geometries where the resulting spatiotemporal pattern is constrained by the boundary conditions. Here we study the Faraday instability in domains with flexible boundaries. This is implemented by triggering this instability in floating fluid drops. An interaction of Faraday waves with the shape of the drop is observed, the radiation pressure of the waves exerting a force on the surface tension held boundaries. Two regimes are observed. In the first one there is a coadaptation of the wave pattern with the shape of the domain so that a steady configuration is reached. In the second one the radiation pressure dominates and no steady regime is reached. The drop stretches and ultimately breaks into smaller domains that have a complex dynamics including spontaneous propagation.     

Spatiotemporal structure of traffic flow in a system with an open boundary

The spatiotemporal structure of a traffic flow pattern is investigated under the open boundary condition using the optimal velocity model. The parameter region where the uniform solution is convectively unstable is determined. It is found that a localized perturbation triggers a linearly unstable oscillatory solution out of the linearly unstable uniform state, and it is shown that the oscillatory solution is also convectively stabilized. It is demonstrated that the observed traffic pattern near an on-ramp can be interpreted as the noise sustained structure in the open flow system.     

A coupled map lattice model for rheological chaos in sheared nematic liquid crystals

A variety of complex fluids under shear exhibit complex spatiotemporal behavior, including what is now termed rheological chaos, at moderate values of the shear rate. Such chaos associated with rheological response occurs in regimes where the Reynolds number is very small. It must thus arise as a consequence of the coupling of the flow to internal structural variables describing the local state of the fluid. We propose a coupled map lattice model for such complex spatiotemporal behavior in a passively sheared nematic liquid crystal using local maps constructed so as to accurately describe the spatially homogeneous case. Such local maps are coupled diffusively to nearest and next-nearest neighbors to mimic the effects of spatial gradients in the underlying equations of motion. We investigate the dynamical steady states obtained as parameters in the map and the strength of the spatial coupling are varied, studying local temporal properties at a single site as well as spatiotemporal features of the extended system. Our methods reproduce the full range of spatiotemporal behavior seen in earlier one-dimensional studies based on partial differential equations. We report results for both the one- and two-dimensional cases, showing that spatial coupling favors uniform or periodically time-varying states, as intuitively expected. We demonstrate and characterize regimes of spatiotemporal intermittency out of which chaos develops. Our work indicates that similar simplified lattice models of the dynamics of complex fluids under shear should provide useful ways to access and quantify spatiotemporal complexity in such problems, in addition to representing a fast and numerically tractable alternative to continuum representations.     

Chimera dynamics in nonlocally coupled moving phase oscillators

Chimera states, a symmetry-breaking spatiotemporal pattern in nonlocally coupled dynamical units, prevail in a variety of systems. However, the interaction structures among oscillators are static in most of studies on chimera state. In this work, we consider a population of agents. Each agent carries a phase oscillator. We assume that agents perform Brownian motions on a ring and interact with each other with a kernel function dependent on the distance between them. When agents are motionless, the model allows for several dynamical states including two different chimera states (the type-I and the type-II chimeras). The movement of agents changes the relative positions among them and produces perpetual noise to impact on the model dynamics. We find that the response of the coupled phase oscillators to the movement of agents depends on both the phase lag α, determining the stabilities of chimera states, and the agent mobility D. For low mobility, the synchronous state transits to the type-I chimera state for α close to π/2 and attracts other initial states otherwise. For intermediate mobility, the coupled oscillators randomly jump among different dynamical states and the jump dynamics depends on α. We investigate the statistical properties in these different dynamical regimes and present the scaling laws between the transient time and the mobility for low mobility and relations between the mean lifetimes of different dynamical states and the mobility for intermediate mobility.