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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2510.18698 |
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| _version_ | 1866915567739338752 |
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| author | Yi, Taishan Zhao, Xiao-Qiang |
| author_facet | Yi, Taishan Zhao, Xiao-Qiang |
| contents | In this paper, under an abstract setting we establish the spreading properties and the existence, non-existence and global attractivity of spatially heterogeneous steady states for a large class of monotone evolution systems without the translational monotonicity under the assumption that one limiting system has both leftward and rightward spreading speeds and the other one has the uniform asymptotic annihilation. Then we apply the developed theory to study the global dynamics of asymptotically homogeneous integro-difference equations, and provide a counter-example to show that the value of the nonlinear function at the finite range of location may give rise to nontrivial fixed points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_18698 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spatio-temporal dynamics for a class of monotone evolution systems Yi, Taishan Zhao, Xiao-Qiang Dynamical Systems Analysis of PDEs Monotone systems, asymptotic translation invariance, steady states, spreading properties, traveling waves In this paper, under an abstract setting we establish the spreading properties and the existence, non-existence and global attractivity of spatially heterogeneous steady states for a large class of monotone evolution systems without the translational monotonicity under the assumption that one limiting system has both leftward and rightward spreading speeds and the other one has the uniform asymptotic annihilation. Then we apply the developed theory to study the global dynamics of asymptotically homogeneous integro-difference equations, and provide a counter-example to show that the value of the nonlinear function at the finite range of location may give rise to nontrivial fixed points. |
| title | Spatio-temporal dynamics for a class of monotone evolution systems |
| topic | Dynamical Systems Analysis of PDEs Monotone systems, asymptotic translation invariance, steady states, spreading properties, traveling waves |
| url | https://arxiv.org/abs/2510.18698 |