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Date:
Aug.1-26 (every Mondays~Wednesdays)
Goals of this course:
Reaction-diffusion systems provide a way to model the movement, mortality, and reproduction of species. From such system, we intend to get conclusions about extinction/persistence of populations, and the coexistence of interacting species. The evolution process of biological systems usually involves the steady states and the waves. In this mini-course, we will introduce some mathematical tools, and then apply these methods to some practical models. The following topics will be covered.
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Reaction-diffusion equations modeling interactions of populations in bounded habitats;
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Wave theories in reaction-diffusion systems
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Free boundary problems in reaction-diffusion systems
Speakers:
(i) Aug.1-3, 2016
Professor Feng-Bin Wang (Chang Gung University)
Title:Reaction-diffusion equations modeling interactions of populations in bounded habitats
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Theory of monotone dynamical system and its applications
Time: 11:00-12:00,14:00-16:00, August 1, 2016
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Theory of uniform persistence and its applications
Time: 10:00-12:00,14:00-15:00, August 2, 2016
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Reaction-diffusion equations in river ecosystems
Time: 10:00-12:00,14:00-15:00, August 3, 2016
(ii) Aug. 8-10, 2016
Professor Chang-Hong Wu (National University of Tainan)
Title:The spreading of invasive species determined by free boundary problems
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Some fundamental results of free boundary problems for parabolic equations
Time : 11:00-12:00,14:00-16:00, August 8, 2016
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Some free boundary problems arising in ecology I
Time : 10:00-12:00,14:00-15:00, August 9, 2016
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Some free boundary problems arising in ecology II
Time : 10:00-12:00,14:00-15:00, August 10, 2016
(iii) Aug. 15-17, 2016
Professor Yaping Wu (Capital Normal University)
Title:Stability of traveling waves for nonlinear evolutional equations
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Spectral theories on linear differential operators
Time : 11:00-12:00,14:00-16:00, August 15, 2016
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Abstract results on the existence and analyticity of Evans functions
Time : 10:00-12:00,14:00-15:00, August 16, 2016
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Extension of Evans function theories and nonlinear stability theories.
Time : 10:00-12:00,14:00-15:00, August 17, 2016
(iv) Aug. 22-24, 2016
Professor Jui-Pin Tseng (National Chengchi University)
Title:Collective dynamics for network systems coupled with delays
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Introduction to the sequential contracting approach
Time: 11:00-12:00,14:00-16:00, August 22, 2016
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Synchronization in nonlinearly coupled network systems with delays.
Time: 10:00-12:00,14:00-15:00, August 23, 2016
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Multistability in nonlinearly coupled network systems with delays.
Time: 10:00-12:00,14:00-15:00, August 24, 2016
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