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Full-Text Articles in Physical Sciences and Mathematics
Locust Dynamics: Behavioral Phase Change And Swarming, Chad M. Topaz, Maria R. D'Orsogna, Leah Edelstein-Keshet, Andrew J. Bernoff
Locust Dynamics: Behavioral Phase Change And Swarming, Chad M. Topaz, Maria R. D'Orsogna, Leah Edelstein-Keshet, Andrew J. Bernoff
Chad M. Topaz
Locusts exhibit two interconvertible behavioral phases, solitarious and gregarious. While solitarious individuals are repelled from other locusts, gregarious insects are attracted to conspecifics and can form large aggregations such as marching hopper bands. Numerous biological experiments at the individual level have shown how crowding biases conversion towards the gregarious form. To understand the formation of marching locust hopper bands, we study phase change at the collective level, and in a quantitative framework. Specifically, we construct a partial integrodifferential equation model incorporating the interplay between phase change and spatial movement at the individual level in order to predict the dynamics of …
Instabilities And Patterns In Coupled Reaction-Diffusion Layers, Anne J. Catlla, Amelia Mcnamara, Chad M. Topaz
Instabilities And Patterns In Coupled Reaction-Diffusion Layers, Anne J. Catlla, Amelia Mcnamara, Chad M. Topaz
Chad M. Topaz
We study instabilities and pattern formation in reaction-diffusion layers that are diffusively coupled. For two-layer systems of identical two-component reactions, we analyze the stability of homogeneous steady states by exploiting the block symmetric structure of the linear problem. There are eight possible primary bifurcation scenarios, including a Turing-Turing bifurcation that involves two disparate length scales whose ratio may be tuned via the interlayer coupling. For systems of n-component layers and nonidentical layers, the linear problem’s block form allows approximate decomposition into lower-dimensional linear problems if the coupling is sufficiently weak. As an example, we apply these results to a two-layer …