THE IDENTIFICATION OF COMPLEX SPATIOTEMPORAL PATTERNS USING COUPLED MAP LATTICE MODELS

A highly efficient, low-order model for vortex-induced vibration of flexible cables at low Reynolds number has been developed. A coupled map lattice (CML) wake model, based on circle maps, is combined with a cable model (linear wave equation). With this model, both the self-excited response of the cable oscillation in the crossflow direction and the resulting wake structures are examined at Re = 100. This represents an improvement over earlier CML models capable of only modelling wakes behind externally forced cables. For comparison, spectral-element based numerical simulations, in addition to experiments on a freely vibrating cable flow, were conducted. The freely vibrating CML model predicted lace-like structures consistent with these numerical simulations and experimental results. Little difference was noted between the vortex shedding wake patterns determined for forced cables (from previous CML models) and freely vibrating cables. The freely vibrating CML matched experimental data for maximum cable amplitude reasonably well over a range of mass-damping parameter employed in offshore structural applications.

Adaptive control of spatiotemporal chaos in coupled map lattices

The topic of utilizing coupled map lattice to investigate complex spatiotemporal dynamics has attracted a lot of interest. For exploring the spatiotemporal complexity of a predator‐prey system with migration and diffusion, a new three‐chain coupled map lattice model is developed in this research. Based on Turing instability analysis, pattern formation conditions for the predator‐prey system are derived. Via numerical simulation, rich Turing patterns are found with subtle self‐organized structures under diffusion‐driven and migration‐driven mechanisms. With the variation of migration rates, the predator‐prey system exhibits a gradual dynamical transition from diffusion‐driven patterns to migration‐driven patterns. Moreover, new results, the self‐organization of non‐Turing patterns, are also revealed. We find that even in the cases where the nonspatial predator‐prey system reaches collapse, the migration can still drive pattern self‐organization. These non‐Turing patterns suggest many new possible ways for the coexistence of predator and prey in space, under the effects of migration and diffusion.

An adaptive wavelet neural network for spatio-temporal system identification

Phase diagrams in unidirectionally coupled map lattice for open traffic flow

Periodic orbits and long transients in coupled map lattices

Common environmental and operational interruptions can lead to station or line failures, which in turn trigger cascading failures in the urban rail transit network (URTN). However, most studies neglect the effects of passenger transfer and attrition behaviours on network resilience under cascading failures. As the primary service recipients of the URTN, passengers have a direct impact on network resilience. Thus, the omission of passenger attrition and transfer behaviour can lead to an overestimated impact of cascading failures. Therefore, this study proposes an improved coupled map lattice (CML) model that integrates passenger transfer and attrition behaviours, station risk resistance, and inter‐node coupling to capture the dynamic evolution of cascading failures. Then, a dual‐metric evaluation framework covering spatial and temporal characteristics is used to assess spatiotemporal resilience. A case study of the Tianjin URTN reveals that different attack strategies and disturbance intensities significantly influence resilience, particularly during morning peak hours, and a critical disturbance threshold of R = 2.2 can trigger large‐scale failure. Additionally, the resilience of the URTN is more significantly influenced by stations with higher connectivity than with higher passenger volume. The findings can provide crucial guidance for emergency planning, thus improving the stability of the URTN.

A family of coupled map lattice (CML) models has been developed to simulate the evolutional mechanism of interactions of convection, diffusion, and dispersion in both weakly and strongly coupled cases. Not only coherent and turbulent properties as well as their relations, but also the transitional states between convection dominating, diffusion dominating and dispersion dominating are analyzed to demonstrate the essential characteristics of any state. Numerical results show that the models are capable of simulating both layered coupling and stochastic mechanism, and lead us to understand whether or not turbulence coherent structure is formed by modulation of wave packet. The duality of wave and particle characters of turbulence is illustrated in the numerical simulation; a sketch picture is given to explain the questions associated with the turbulent inverse cascade, which is the result of the mutual interactions among the physical factors of nonlinearity, dissipation and dispersion.

In this paper, we discuss the stability and pattern formation issues of a spatiotemporal discrete system based on the modified Klausmeier model. We begin by constructing the corresponding coupled map lattices model. Then the existence and stability analysis is employed to derive the prerequisites for a stable homogeneous stationary state. Through the center manifold theorem and bifurcation theory, the threshold parameter values for flip bifurcation, Neimark–Sacker bifurcation and Turing bifurcation are individually determined. Based on the analysis of bifurcation, four pattern formation mechanisms are presented. Finally, we simulate the corresponding results numerically. The simulations exhibit rich dynamical behaviors, such as period-doubling cascades, invariant cycles, periodic windows, chaos, and rich Turing patterns. Four pattern formation mechanisms give rise to rich and complex patterns, including mosaics, spots, circles, spirals and cyclic fragmentation. The analysis and findings from this study enhance our comprehension of the intricate relationships among bifurcation, chaos and pattern formation for the spatiotemporal discrete Klausmeier model.

Dendrites with developed sidebranches are numerically studied with a coupled map lattice model. The competitive dynamics among sidebranches determines the shape of the envelope. The envelope has a parabolic shape near the tip of the dendrite and the envelope angle with respect to the main branch increases up to 45$^{\circ}$ finally. In an intermediate region, the envelope grows roughly in a power law, however, the exponent increases gradually as a function of the distance from the tip. The competitive dynamics among many branches is also observed in a unidirectional growth from a linear seed, and it is compared with the competitive dynamics of sidebranches.

In recent years, there is growing literature concerning the cascading failure of network characteristics. The object of this paper is to investigate the cascade failures on road traffic network, considering the aeolotropism of road traffic network topology and road congestion dissipation in traffic flow. An improved coupled map lattice (CML) model is proposed. Furthermore, in order to match the congestion dissipation, a recovery mechanism is put forward in this paper. With a real urban road traffic network in Beijing, the cascading failures are tested using different attack strategies, coupling strengths, external perturbations, and attacked road segment numbers. The impacts of different aspects on road traffic network are evaluated based on the simulation results. The findings confirmed the important roles that these characteristics played in the cascading failure propagation and dissipation on road traffic network. We hope these findings are helpful to find out the optimal road network topology and avoid cascading failure on road network.

Mechanisms for potential oscillations and synchronizing self-organized formation of ordered dendrite structures, which is an important example of morphogenesis in Laplacian fields, were studied using Sn, Zn, Cu, and Pb electrodeposition. Electron backscattering diffraction (EBSD) experiments showed that Sn latticework as a typical example of the ordered dendrite structures grew in an epitaxial mode in particular directions from the Sn electrode surface. In situ optical and phase-contrast microscopic inspection showed that the Sn latticework growth as well as the concentration profile for deposited Sn(II) ions near the growing front oscillated in synchronization with the potential oscillation, which led to formation of a highly ordered Sn latticework structure. Similar behavior was observed in other electrodeposition systems. On the basis of these results, a general mechanism for the potential oscillations and synchronized formation of the ordered dendrite structures was proposed, in which autocatalytic crystal growth, passivation in flat surfaces of dendrites, and depletion of deposited metal ions in the electrolyte near and inside the dendrites played the key roles. Numerical calculations by use of a modified coupled map lattice (CML) model confirmed the validity of the mechanism. The clarification of the general mechanism has enabled us to classify all the oscillatory dendrite growth, including reported ones by other research groups, into three types (type-I, type-II, and type-III), which will serve for preparation of designed and controlled micro- and nanostructures at solid surfaces.

The coupled map lattices (CML) is a spatiotemporal chaotic system with complex dynamic behavior. In this paper, we propose a spatiotemporal chaotic system with a novel pseudo-random coupling method based on elementary cellular automata (ECA), and introduce different perturbations into lattices in each iteration according to ECA. We investigate the spatiotemporal dynamic properties and chaotic behaviors of the proposed system such as bifurcation diagrams, Kolmogorov Sinai entropy, and uniformity. Moreover, the randomness of sequences generated by the proposed system and the correlation between any two lattices are discussed. Theory analyses and simulations indicate that the new system has better performance in complexity, ergodic and unpredictability than other CML systems such as adjacent CML and nonlinear CML based on fractional order logistic equation, etc. Furthermore, the correlation coefficient between any two lattices in the proposed system is significantly lower than other systems, and another advantage of the proposed system is utilizing the output of ECA to perturb the chaotic system which can effectively alleviate the dynamical degradation in digital system. The excellent performance of the proposed system demonstrates that it has great potential for crypto-system.

The Kolmogorov-Sinai entropy of the Ising model is calculated with a coupled map lattice model. The KS entropy indicates a mixing rate in the equilibrium state. The KS entropy exhibits a similar type of singularity to the Boltzmann entropy at the critical point.

A model of metal electrodeposition within mesoporous silicon is proposed. The model is based on the coupled map lattice model, which includes diffusion of metal ions, electrode shape, equivalent circuit of electrochemical cell, and potential drop in porous silicon wall. Continuous filling from the pore bottom to the opening and plugging at the pore opening were successfully reproduced using the present model. By analyzing the concentration profile of cupric ions in solution, the mechanism of plugging at the pore opening and discontinuous filling by electrodeposition is discussed.