arXiv subjects

Jiawei Chu

Publications and source records attributed to Jiawei Chu.

4 recordsLinked to original sources

arXiv2026

Parabolic-elliptic reduction suppresses Hopf bifurcation in a forager-exploiter system with cascade taxis

We study a parabolic-elliptic forager-exploiter model describing the cascade interaction between two species through a shared environmental resource with a constant renewal rate. We first establish the global existence and uniform boundedness of classical solutions in arbitrary dimensions {\color{black}for large initial population data and large taxis sensitivity coefficients. We then investigate the long-time behavior of solutions.} When the resource renewal rate is small, all solutions will converge exponentially to the unique constant steady state. Furthermore, for large resource renewal rates, the parabolic-elliptic system does not undergo Hopf bifurcation, which is in sharp contrast to the corresponding fully parabolic case, where temporal oscillations arise via Hopf bifurcation.

math.AP↗

arXiv2026

Periodic dynamics in a forager-exploiter system under homogeneous and heterogeneous resource environments

We investigate time-periodic dynamics in a forager-exploiter system with a taxis cascade under both homogeneous and heterogeneous resource environments. The model describes the interactions among foragers, exploiters, and environmental resources, where foragers move toward higher resource densities while exploiters aggregate toward regions with higher forager densities. Our results show that different resource renewal mechanisms shape periodic dynamics in fundamentally different ways. Precisely, for time-periodic resource renewal rates, we establish the existence of positive time-periodic solutions for any positive renewal rate and further prove their global stability under suitable conditions on the parameters. In contrast, for homogeneous environments, only large resource renewal rates can destabilize the constant steady state through the Hopf bifurcation, thereby generating non-constant time-periodic solutions. Interestingly, for spatially heterogeneous and temporally homogeneous environments, our numerical simulations indicate that spatial heterogeneity exhibits opposing effects on periodic dynamics depending on total resource availability. When resources are sufficiently abundant, spatial heterogeneity tends to suppress the emergence of temporal oscillations, whereas when resources are relatively scarce, it may instead promote oscillatory behaviors, and sufficiently concentrated local resource supplies can trigger local or even global temporal oscillations. These findings reveal a delicate interplay among resource renewal mechanisms, resource availability, and spatial heterogeneity in shaping dynamics behavior.

math.AP↗

arXiv2024

An Optimal Switching Approach for Bird Migration

Bird migration is an adaptive behavior ultimately aiming at optimizing survival and reproductive success. We propose an optimal switching model to study bird migration, where birds' migration behaviors can be efficiently modeled as switching between different stochastic differential equations. For individuals with perfect information regarding the environment, we implement numeric methods to see the expected payoff and corresponding optimal control. For individual with only partial information of the environment, we combine the finite difference method and stochastic simulations to investigate the change of the bird's optimal strategy. Based on biological backgrounds, we characterizing the optimal strategies of birds under different scenarios and these behaviors depend on the specific assumptions of the model.

math.OC↗

arXiv2021

Global dynamics in a chemotaxis model describing tumor angiogenesis with/without mitosis in any dimensions

In this work, we study the Neumann initial boundary value problem for a three-component chemotaxis model in any dimensional bounded and smooth domains; this model is used to describe the branching of capillary sprouts during angiogenesis. First, we find three qualitatively simple sufficient conditions for qualitative global boundedness, and then, we establish two types of global stability for bounded solutions in qualitative ways. As a consequence of our findings, the underlying system without chemotaxis and the effect of ECs mitosis can not give rise to pattern formations. Our findings quantify and extend significantly previous studies, which are set in lower dimensional convex domains and are with no qualitative information.

math.AP↗