Nikos Kouvaris ( University Pompeu Fabra)

Title: Pattern formation in bistable networks: Theory and applications to chemical reactions

Abstract:

Self-organization processes in complex networks is an interdisciplinary research field with great theoretical interest and many potential applications in chemistry and biology. Stationary localized patterns constitute a classical example of self-organization; they can spontaneously be generated by the Turing mechanism, as it has been reported in both continuous and networked media. However, an alternative mechanism for the emergence of stationary patterns in networks was recently discovered [1-4]. We have experimentally demonstrated and theoretically analyzed that bistable networks can support a rich variety of stationary patterns determined by the network architecture and the initial conditions [2,3]. By applying a localized perturbation to a network node or a subset of nodes, 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. Weak coupling results in trivial pinned states where the activation is stationary. At strong coupling, a uniform state is expected with active or inactive elements at small or large nodes degree, respectively. Nontrivial stationary spatial patterns, corresponding to an activation pinning, are predicted to occur at nodes with intermediate degrees and at intermediate coupling strengths. The results are confirmed in experiments with networks of coupled bistable electrochemical reactions. Although our experimental system is actually more complex than the simplifying assumptions under which the theory was constructed, the results show a surprisingly good agreement. This indicates that the found pattern formation mechanism is robust and generic.

In this talk we discuss theoretical and experimental studies with bistable chemical reactions organized in tree [1,2] and star [3] networks. These results are relevant for large random networks [2]. Mechanisms for the control and deliberate design of such patterns [4] will also be considered.

References:
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1. N. E. Kouvaris, H. Kori and A. S. Mikhailov, PLoS ONE 7, e45029 (2012).
2. N. E. Kouvaris, M. Sebek, A. S. Mikhailov and I. Z. Kiss, Angew. Chem. Int. Ed., 55, 13267-13270 (2016).
3. N. E. Kouvaris, M. Sebek, A. Iribarne, A. Diaz-Guilera and I. Z. Kiss, Phys. Rev. E 95, 042203 (2017).
4. N. E. Kouvaris and A. S. Mikhailov, Europhys. Lett. 102, 16003 (2013).