A local PDE model of aggregation formation in bacterial colonies

Chavy-Waddy, P. C.; Kolokolnikov, Théodore

doi:10.1088/0951-7715/29/10/3174

Cited by 11 publications

(14 citation statements)

References 28 publications

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“…In synchronizing systems, the dynamic state variables are the oscillators' phases, whose influence on each other leads to macro-level temporal structures (synchrony). A similar effect occurs in swarming [17][18][19][20][21][22][23][24][25][26], a phenomenon as widespread as synchronization, as evidenced by flocks of birds, [27,28] locust swarms, [29][30][31] bacterial aggregation, [32][33][34] schools of fish, [35,36], predator-prey interactions, [37,38], self-assembly [39][40][41][42][43], and even the vortices of Bose-Einstein condensates [44][45][46][47][48]. Like synchronizing oscillators, the interactions between swarming particles gives rise to group-level structures.…”

Section: Introductionmentioning

confidence: 89%

Ring states in swarmalator systems

2018

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Synchronization is a universal phenomenon, occurring in systems as disparate as Japanese tree frogs and Josephson junctions. Typically, the elements of synchronizing systems adjust the phases of their oscillations, but not their positions in space. The reverse scenario is found in swarming systems, such as schools of fish or flocks of birds; now the elements adjust their positions in space, but without (noticeably) changing their internal states. Systems capable of both swarming and synchronizing, dubbed swarmalators, have recently been proposed, and analyzed in the continuum limit. Here, we extend this work by studying finite populations of swarmalators, whose phase similarity affects both their spatial attraction and repulsion. We find ring states, and compute criteria for their existence and stability. Larger populations can form annular distributions, whose density we calculate explicitly. These states may be observable in groups of Japanese tree frogs, ferromagnetic colloids, and other systems with an interplay between swarming and synchronization.

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Section: Introductionmentioning

confidence: 89%

Ring states in swarmalator systems

2018

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“…F att and F rep represent the influence of phase similarity on spatial attraction and repulsion, respectively. In equation (2), phase interaction between the swarmalators is controlled by the function H and the influence of spatial proximity on phase dynamics is given by G. Swarmalators' phases are coupled with strength ε ∈ R. When ε is positive (attractive coupling), swarmalators try to minimize their phase differences while a negative value (repulsive coupling) of ε increases the incoherence of their phases. In reference [39], three stationary (one each for attractive, repulsive, and absence of phase coupling) and two non-stationary states (both for repulsive phase coupling) of possible long-term aggregation are found.…”

Section: Introductionmentioning

confidence: 99%

“…One of the most common attributes among different organisms in nature is to dwell in groups or move in consensus and mimic the activities of their local neighbors, the reason of which can be traced back to the survival instinct of those organisms. The examples of which can be found in systems as small as bacterial aggregation [1,2] to macro-organisms such as flock of birds, herd of sheep, and school of fish [3][4][5][6][7][8]. In all these systems, the individuals organize their positions in space to aggregate together or move in unison.…”

Section: Introductionmentioning

confidence: 99%

Swarmalators under competitive time-varying phase interactions

et al. 2022

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Swarmalators are entities with the simultaneous presence of swarming and synchronization that reveal emergent collective behavior due to the fascinating bidirectional interplay between phase and spatial dynamics. Although different coupling topologies have already been considered, here we introduce time-varying competitive phase interaction among swarmalators where the underlying connectivity for attractive and repulsive coupling varies depending on the vision (sensing) radius. Apart from investigating some fundamental properties like conservation of center of position and collision avoidance, we also scrutinize the cases of extreme limits of vision radius. The concurrence of attractive-repulsive competitive phase coupling allows the exploration of diverse asymptotic states, like static $\pi$, and mixed phase wave states, and we explore the feasible routes of those states through a detailed numerical analysis. In sole presence of attractive local coupling, we reveal the occurrence of static cluster synchronization where the number of clusters depends crucially on the initial distribution of positions and phases of each swarmalator. In addition, we analytically calculate the sufficient condition for the emergence of the static synchronization state. We further report the appearance of the static ring phase wave state and evaluate its radius theoretically. Finally, we validate our findings using Stuart-Landau oscillators to describe the phase dynamics of swarmalators subject to attractive local coupling.

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Section: Introductionmentioning

confidence: 99%

Swarmalators under competitive time-varying phase interactions

Sar,

Chowdhury,

Perc

et al. 2022

Preprint

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A local PDE model of aggregation formation in bacterial colonies

Abstract: We study pattern formation in a model of cyanobacteria motion recently proposed by Galante, Wisen, Bhaya and Levy. By taking a continuum limit of their model, we derive a novel fourth-order nonlinear parabolic PDE equation that governs the behaviour of the model. This PDE is

Cited by 11 publications

References 28 publications

Ring states in swarmalator systems

Ring states in swarmalator systems

Swarmalators under competitive time-varying phase interactions

Swarmalators under competitive time-varying phase interactions

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