Selection of spatiotemporal patterns in arrays of spatially distributed oscillators indirectly coupled via a diffusive environment

Cao, Xiao-Zhi; He, Yuan; Li, Bingwei

doi:10.1063/1.5058741

Cited by 6 publications

(4 citation statements)

References 39 publications

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“…The PDE-ODE framework of (1.0.1), where the small signaling compartments are modeled explicitly, also provides an alternative approach for studying large-scale self-organized structures that have previously been modeled through PDE-ODE lattice dynamics in which the dynamically active "cells" are treated as point sources restricted to lattice sites and where a discrete Laplacian averaging over nearby lattice points replaces the Laplace operator (cf. [6], [43], [29]). Such lattice PDE-ODE systems have been used to model traveling waves of yeast activation due to substrate addition of glucose at a localized source (cf.…”

Section: Discussion and Outlookmentioning

confidence: 99%

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Synchrony and Oscillatory Dynamics for a 2-D PDE-ODE Model of Diffusion-Sensing with Small Signaling Compartments

Iyaniwura,

Ward

2020

Preprint

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We analyze a class of cell-bulk coupled PDE-ODE models, motivated by quorum and diffusion sensing phenomena in microbial systems, that characterize communication between localized spatially segregated dynamically active signaling compartments or "cells" that have a permeable boundary. In this model, the cells are disks of a common radius ε 1 and they are spatially coupled through a passive extracellular bulk diffusion field with diffusivity D in a bounded 2-D domain. Each cell secretes a signaling chemical into the bulk region at a constant rate and receives a feedback of the bulk chemical from the entire collection of cells. This global feedback, which activates signaling pathways within the cells, modifies the intracellular dynamics according to the external environment. The cell secretion and global feedback are regulated by permeability parameters across the cell membrane. For arbitrary reaction-kinetics within each cell, the method of matched asymptotic expansions is used in the limit ε 1 of small cell radius to construct steady-state solutions of the PDE-ODE model, and to derive a globally coupled nonlinear matrix eigenvalue problem (GCEP) that characterizes the linear stability properties of the steady-states. The analysis and computation of the nullspace of the GCEP as parameters are varied is central to the linear stability analysis. In the limit of large bulk diffusivity D = D0/ν 1, where ν ≡ −1/ log ε, an asymptotic analysis of the PDE-ODE model leads to a limiting ODE system for the spatial average of the concentration in the bulk region that is coupled to the intracellular dynamics within the cells. Results from the linear stability theory and ODE dynamics are illustrated for Sel'kov reaction-kinetics, where the kinetic parameters are chosen so that each cell is quiescent when uncoupled from the bulk medium. For various specific spatial configurations of cells, the linear stability theory is used to construct phase diagrams in parameter space characterizing where a switch-like emergence of intracellular oscillations can occur through a Hopf bifurcation. The effect of the membrane permeability parameters, the reaction-kinetic parameters, the bulk diffusivity, and the spatial configuration of cells on both the emergence and synchronization of the oscillatory intracellular dynamics, as mediated by the bulk diffusion field, is analyzed in detail. The linear stability theory is validated from full numerical simulations of the PDE-ODE system, and from the reduced ODE model when D is large.

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Section: Discussion and Outlookmentioning

confidence: 99%

“…[43]), and the emergence of spiral waves resulting from the coupling of Fitzhugh-Nagumo or Rossler cell kinetics to discrete lattice-based diffusion (cf. [29], [6]).…”

Section: Discussion and Outlookmentioning

confidence: 99%

Synchrony and Oscillatory Dynamics for a 2-D PDE-ODE Model of Diffusion-Sensing with Small Signaling Compartments

Iyaniwura,

Ward

2020

Preprint

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“…A. The Stuart-Landau oscillator model with the environmental coupling A general model that represents a large population of oscillators coupled via a diffusive environment usually reads [66,67,78,79],…”

Section: Spiral Wave Chimeras In An Environmentally Coupled Stuart-la...mentioning

confidence: 99%

Spiral wave chimera states in populations of oscillators mediated by a slowly varying diffusive environment

Yang¹,

He²,

2021

Preprint

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Chimera states are usually observed in oscillator systems with nonlocal couplings. Such a nonlocal coupling arises typically as oscillators are coupled via an external environment which changes so fast that it could be eliminated adiabatically. Here we for the first time report the existence of spiral wave chimera states in large populations of Stuart-Landau oscillators coupled via a slowly changing diffusive environment under which the adiabatic approximation breaks down. The transition from spiral wave chimeras to spiral waves with the smooth core and to unstable spiral wave chimeras as functions of the system parameters are exploited. The phenomenological mechanism for explaining the formation of spiral wave chimeras is also proposed. The existence of spiral wave chimeras and the underlying mechanism are further confirmed in a three-component FitzHugh-Nagumo system with the similar environmental coupling scheme. Our results provide important hints to seek chimera patterns in both laboratory and realistic chemical or biological systems.

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“…We first note that the RD system described by Eqs. (1-3) can be treated as a population of FHN oscillators (each has two variables, u and v) coupled indirectly through a common medium (described by w) [59,79,80]. In this picture, the local oscillators are isolated from each other, but are all driven by a spatially extended dynamical medium.…”

Section: Mechanism Analysismentioning

confidence: 99%

Spiral wave chimeras in reaction-diffusion systems: phenomenon, mechanism and transitions

Li,

He,

et al. 2020

Preprint

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Spiral wave chimeras (SWCs), which combine the features of spiral waves and chimera states, are a new type of dynamical patterns emerged in spatiotemporal systems due to the spontaneous symmetry breaking of the system dynamics. In generating SWC, the conventional wisdom is that the dynamical elements should be coupled in a nonlocal fashion. For this reason, it is commonly believed that SWC is excluded from the general reaction-diffusion (RD) systems possessing only local couplings. Here, by an experimentally feasible model of three-component FitzHugh-Nagumo-type RD system, we demonstrate that, even though the system elements are locally coupled, stable SWCs can still be observed in a wide region in the parameter space. The properties of SWCs are explored, and the underlying mechanisms are analyzed from the point view of coupled oscillators. Transitions from SWC to incoherent states are also investigated, and it is found that SWCs are typically destabilized in two scenarios, namely core breakup and core expansion. The former is characterized by a continuous breakup of the single asynchronous core into a number of small asynchronous cores, whereas the latter is featured by the continuous expansion of the single asynchronous core to the whole space. Remarkably, in the scenario of core expansion, the system may develop into an intriguing state in which regular spiral waves are embedded in a completely disordered background. This state, which is named shadowed spirals, manifests from a new perspective the coexistence of incoherent and coherent states in spatiotemporal systems, generalizing therefore the traditional concept of chimera states. Our studies provide an affirmative answer to the observation of SWCs in RD systems, and pave a way to the realization of SWCs in experiments.

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Selection of spatiotemporal patterns in arrays of spatially distributed oscillators indirectly coupled via a diffusive environment

Cited by 6 publications

References 39 publications

Synchrony and Oscillatory Dynamics for a 2-D PDE-ODE Model of Diffusion-Sensing with Small Signaling Compartments

Synchrony and Oscillatory Dynamics for a 2-D PDE-ODE Model of Diffusion-Sensing with Small Signaling Compartments

Spiral wave chimera states in populations of oscillators mediated by a slowly varying diffusive environment

Spiral wave chimeras in reaction-diffusion systems: phenomenon, mechanism and transitions

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