Dynamical analysis in a nonlocal delayed reaction-diffusion tumor model with therapy
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915678291755008 |
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| author | Hu, Dandan Yuan, Yuan |
| author_facet | Hu, Dandan Yuan, Yuan |
| contents | In this work, we investigate the dynamical properties of a reaction-diffusion system arising from tumor-therapy modelling that features both nonlinear interactions and nonlocal delay. By applying the Lyapunov-Schmidt reduction, we establish the existence of a nontrivial steady-state solution bifurcating from the trivial solution. In particular, we derive an approximate expression for a spatially nonhomogeneous steady-state solution. Then, we provide a detailed spectral characterization of the linearized operator and explicit stability criteria and identify the delay-dependent Hopf bifurcation regimes. To illustrate the theoretical results, we include a concrete example that verifies the claims in our theorems and numerically demonstrates how changes in treatment parameters alter stability and bifurcation behaviour. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_13831 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamical analysis in a nonlocal delayed reaction-diffusion tumor model with therapy Hu, Dandan Yuan, Yuan Dynamical Systems 34K18, 35B32, 35B35, 35K57, 35Q92 In this work, we investigate the dynamical properties of a reaction-diffusion system arising from tumor-therapy modelling that features both nonlinear interactions and nonlocal delay. By applying the Lyapunov-Schmidt reduction, we establish the existence of a nontrivial steady-state solution bifurcating from the trivial solution. In particular, we derive an approximate expression for a spatially nonhomogeneous steady-state solution. Then, we provide a detailed spectral characterization of the linearized operator and explicit stability criteria and identify the delay-dependent Hopf bifurcation regimes. To illustrate the theoretical results, we include a concrete example that verifies the claims in our theorems and numerically demonstrates how changes in treatment parameters alter stability and bifurcation behaviour. |
| title | Dynamical analysis in a nonlocal delayed reaction-diffusion tumor model with therapy |
| topic | Dynamical Systems 34K18, 35B32, 35B35, 35K57, 35Q92 |
| url | https://arxiv.org/abs/2512.13831 |