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arXiv · 2608.07701

Transient instability and recurrent aggregation in a two-species chemotaxis-competition system under environmental periodicity

Federico Herrero-Hervás·Pedro Hernández-Alonso·Mihaela Negreanu
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Abstract

This work investigates recurrent pattern formation in a two--species chemotaxis system with competitive dynamics under the assumption that the carrying capacities of both species are periodic in time. By considering a globally attracting periodic solution to the associated nonautonomous ODE system as a spatially homogeneous base state, we derive sufficient conditions for the existence of a critical chemotactic sensitivity of the first species, denoted by $χ_{\text{crit}}$. Whenever this threshold is exceeded, the periodic state becomes linearly unstable over a nonempty set of times within each environmental cycle. This gives rise to a recurrent alternation of unstable and stable intervals, during which spatial perturbations are respectively amplified and damped. The analytical derivation is complemented with numerical simulations, in both periodic coexistence and competitive exclusion regimes. Finally, we discuss the temporal location of the instability sets and the possibility of negative instability thresholds.

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Federico Herrero-Hervás, Pedro Hernández-Alonso, Mihaela Negreanu. 2026-08-07. Transient instability and recurrent aggregation in a two-species chemotaxis-competition system under environmental periodicity. https://arxiv.org/abs/2608.07701

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