Uniform-in-time propagation of chaos and bifurcation in two-type adhesion systems
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911512157749248 |
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| author | Chae, Myeongju Choi, Young-Pil |
| author_facet | Chae, Myeongju Choi, Young-Pil |
| contents | We study a nonlocal adhesion model for two interacting tumor cell phenotypes, combining diffusion, pairwise interactions, and random phenotypic switching. The system admits a microscopic diffusion--jump particle description whose mean-field limit is a nonlinear McKean--Vlasov equation on a product space encoding position and internal state. We first establish uniform-in-time propagation of chaos in the weak-interaction regime using a coupling approach that combines reflection coupling for the diffusion with an optimal coupling of the spin-flip dynamics. As a byproduct, we obtain exponential long-time contraction for the nonlinear McKean--Vlasov equation in the first-order Wasserstein distance, implying uniqueness of the stationary distribution. We also investigate the complementary regime of strong interactions, where the homogeneous equilibrium may lose stability through a bifurcation mechanism. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_12802 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Uniform-in-time propagation of chaos and bifurcation in two-type adhesion systems Chae, Myeongju Choi, Young-Pil Analysis of PDEs Probability We study a nonlocal adhesion model for two interacting tumor cell phenotypes, combining diffusion, pairwise interactions, and random phenotypic switching. The system admits a microscopic diffusion--jump particle description whose mean-field limit is a nonlinear McKean--Vlasov equation on a product space encoding position and internal state. We first establish uniform-in-time propagation of chaos in the weak-interaction regime using a coupling approach that combines reflection coupling for the diffusion with an optimal coupling of the spin-flip dynamics. As a byproduct, we obtain exponential long-time contraction for the nonlinear McKean--Vlasov equation in the first-order Wasserstein distance, implying uniqueness of the stationary distribution. We also investigate the complementary regime of strong interactions, where the homogeneous equilibrium may lose stability through a bifurcation mechanism. |
| title | Uniform-in-time propagation of chaos and bifurcation in two-type adhesion systems |
| topic | Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2603.12802 |