Propagation failure and multiple steady states in an array of diffusion coupled flow reactors

Laplante, J. P.; Erneux, Thomas

doi:10.1016/0378-4371(92)90256-p

Cited by 46 publications

(22 citation statements)

References 17 publications

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“…[23] Such elements can have local or diffusive connections between them. For regular lattices and linear chains (i.e., for relatively simple networks), it is known that, under sufficiently weak coupling, the fronts fail to propagate, and thus stationary domains can be formed, [24,25,26,27] whereas at strong coupling the fronts spread [27,28] and a uniform state is eventually established. Recently, analogues phenomena were theoretically investigated for complex networks and the formation of stationary domains, sensitive to the network topology, was predicted based on a simple model of regular trees and onecomponent bistable elements.…”

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confidence: 99%

Self‐Organized Stationary Patterns in Networks of Bistable Chemical Reactions

et al. 2016

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Experiments with a network of bistable electrochemical reactions, organized in regular and non-regular tree networks, are presented to confirm an alternative to Turing mechanism for formation selforganized stationary patterns. The results show that the pattern formation can be described by identification of domains that can be activated individually or in combinations. The method was also demonstrated to localization of chemical reactions to network substructures and identification of critical sites whose activation results in complete activation of the system. While the experiments were performed with a specific nickel electrodissolution system, they reproduce all the salient dynamical behavior of a general network model with a single nonlinearity parameter. This indicates that the considered pattern formation mechanism is very robust and similar behavior can thus be expected in other natural or engineered networked systems, which exhibit, at least locally, a tree-like structure.In biological context, many chemical reactions take place in discrete units, e.g., in cells, that form a complex network. The interplays between local reaction kinetics (nodes), the physical processes that create coupling (link), and the architecture of the network in such systems can lead to a wealth of self-organized phenomena, including synchronization, [4,6,8] stationary Turing and oscillatory patterns, [9,10,11,12,13] or excitation waves. [14,15,16] Stationary patterns generated via the Turing[17] mechanism have been observed in experiments for both continuous [18] and networked [19] systems. Here, an alternative mechanism for emergence of stationary patterns in networks is experimentally explored. We focus on network-organized systems of bistable elements with diffusive connections between them. Bistable elements can be found in a broad class of chemical reactions (e.g., with autocatalysis [20,21]) but also in cellular [22] and engineered systems.[23] Such elements can have local or diffusive connections between them. For regular lattices and linear chains (i.e., for relatively simple networks), it is known that, under sufficiently weak coupling, the fronts fail to propagate, and thus stationary domains can be formed, [24,25,26,27] whereas at strong coupling the fronts spread [27,28] and a uniform state is eventually established. Recently, analogues phenomena were theoretically investigated for complex 1

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confidence: 99%

Self‐Organized Stationary Patterns in Networks of Bistable Chemical Reactions

et al. 2016

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“…In continuous bistable media, traveling fronts, representing waves of transition from one stable state into another can be observed [29,30]. Traveling fronts can become pinned if coupling is sufficiently weak [34][35][36][37][38], forming stationary patterns, in chains and lattices of diffusively coupled bistable elements. Complex tree networks of coupled bistable units, both regular and irregular, exhibit the spreading, retreating or stationary patterns dependent on the coupling strength and the degree distribution of the nodes [5,6,28].…”

Section: Introductionmentioning

confidence: 99%

Stationary patterns in star networks of bistable units: Theory and application to chemical reactions

et al. 2017

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We present theoretical and experimental studies on pattern formation with bistable dynamical units coupled in a star network configuration. By applying a localized perturbation to the central or the peripheral elements, we demonstrate the subsequent spreading, pinning, or retraction of the activations; such analysis enables the characterization of the formation of stationary patterns of localized activity. The results are interpreted with a theoretical analysis of a simplified bistable reaction-diffusion model. Weak coupling results in trivial pinned states where the activation cannot propagate. At strong coupling, a uniform state is expected with active or inactive elements at small or large degree networks, respectively. A nontrivial stationary spatial pattern, corresponding to an activation pinning, is predicted to occur at an intermediate number of peripheral elements and at intermediate coupling strengths, where the central activation of the network is pinned, but the peripheral activation propagates toward the center. The results are confirmed in experiments with star networks of bistable electrochemical reactions. The experiments confirm the existence of the stationary spatial patterns and the dependence of coupling strength on the number of peripheral elements for transitions between pinned and retreating or spreading fronts in forced network configurations (where the central or periphery elements are forced to maintain their states).

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“…The discreteness effects may modify severely the dynamics of the front propagation even in the framework of the simplest models (see the pioneering works of Ishimori & Munakata [14] and Peyrard & Kruskal [15]). The relevant physical contexts can be quite diverse, including hydrogen-bonded chains [16], calcium release waves in living cells [17][18][19], reaction fronts in chains of coupled chemical reactors [20][21][22], arrays of coupled diode resonators [23], semiconductor superlattices [24], discontinuous propagation of action potential in cardiac tissue [25][26][27], arrays of autocrine cells [28], superconductivity in Josephson junctions [29], nonlinear optics and waveguide arrays [30] and the dynamics of neuron chains [31] to mention a few. The dynamics of all these systems is mainly driven by their inherently discrete nature.…”

Section: Introductionmentioning

confidence: 99%

Continuous description of lattice discreteness effects in front propagation

Clerc

Elías

Rojas

2011

Phil. Trans. R. Soc. A.

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Models describing microscopic or mesoscopic phenomena in physics are inherently discrete, where the lattice spacing between fundamental components, such as in the case of atomic sites, is a fundamental physical parameter. The effect of spatial discreteness over front propagation phenomenon in an overdamped one-dimensional periodic lattice is studied. We show here that the study of front propagation leads in a discrete description to different conclusions that in the case of its, respectively, continuous description, and also that the results of the discrete model, can be inferred by effective continuous equations with a supplementary spatially periodic term that we have denominated Peierls-Nabarro drift, which describes the bifurcation diagram of the front speed, the appearance of particle-type solutions and their snaking bifurcation diagram. Numerical simulations of the discrete equation show quite good agreement with the phenomenological description.

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Propagation failure and multiple steady states in an array of diffusion coupled flow reactors

Cited by 46 publications

References 17 publications

Self‐Organized Stationary Patterns in Networks of Bistable Chemical Reactions

Self‐Organized Stationary Patterns in Networks of Bistable Chemical Reactions

Stationary patterns in star networks of bistable units: Theory and application to chemical reactions

Continuous description of lattice discreteness effects in front propagation

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