Nonlocal and Local Interactions in Population Dynamics: Mathematical Analysis and Numerical Approaches.
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Organizer(s): |
Name:
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Affiliation:
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Country:
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Silvia Sastre Gómez
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Universidad de Sevilla
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Spain
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Cristian Morales Rodrigo
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Universidad de Sevilla
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Spain
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Juan Vicente Rodríguez Santacreu
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Universidad de Sevilla
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Spain
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Introduction:
| | Traditional local models in population dynamics are insufficient to capture the full scope of biological realities, as species often respond to cues and interactions over extended spatial ranges. This session emphasizes the importance of incorporating nonlocal terms into population models, reflecting behaviors influenced by external information, resources, or sensory perceptions such as olfactory or visual cues. The inclusion of nonlocal interactions introduces complex mathematical challenges but enriches the dynamical properties of these systems. We will explore recent advances in the analysis of partial differential equations (PDEs) that describe such models, focusing on the existence, uniqueness, regularity, and asymptotic behavior of solutions. Additionally, the session will present numerical methods designed to accurately approximate these equations, emphasizing stability and fidelity to biological phenomena. A particular focus will be on models involving transport terms that simulate chemical attraction or repulsion, further aligning mathematical models with biological processes. By bringing mathematical rigor with biological relevance, this session aims to contribute to the development of robust analytical and computational tools for these complex systems.
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