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Extinction and blow-up phenomena in a non-linear gender structured population model
Institution:1. University of North Alabama, Florence, AL, USA;2. Middle Tennessee State University, Murfreesboro, TN, USA;1. Department of Mathematics, Universitat Autònoma de Barcelona, Bellaterra, 08193, Spain;2. Division of Computing Science and Mathematics, University of Stirling, Stirling, FK9 4LA, United Kingdom;1. Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China;2. Centre for Energy (M473), The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia;1. Department of physics, Azarbaijan Shahid Madani University, Tabriz, Iran;2. Azarbaijan Shahid Madani University, Campus Tabriz, Tabriz, Iran;1. Department of Mechanical Engineering, University of Brawijaya, Veteran Street, Malang, East Java 65145, Indonesia;2. Department of Mechanical Engineering, Yamaguchi University, Ube, Yamaguchi 755-8611, Japan
Abstract:In this article we consider a gender structured model in population dynamics. We assume that the fertility rate depends upon the weighted population of males instead of total population of males. The proportion of males in the population is determined by fixed environmental or social conditions. Here we prove an existence and uniqueness result for a non-trivial steady state. If the initial age distribution is uniformly below the non-trivial steady state then we show that the total population goes extinct in infinite time. On the other hand, if we take the initial age distribution to be uniformly above the steady state then the total population blows up exponentially with time.
Keywords:Age structured population  Two sex models  Non-linear renewal equation  Blow up
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