Abstract
Migration is a key ecological process that enables connections between spatially separated populations. Previous studies have indicated that migration can stabilize chaotic ecosystems. However, the role of migration for two similar types of ecosystems, one chaotic and the other stable, has not yet been studied properly. In the present paper, we investigate the stability of ecological systems that are spatially separated but connected through migration. We consider two similar types of ecosystems that are coupled through migration, where one system shows chaotic dynamics, and other shows stable dynamics. We also note that the direction of the migration is bi-directional and is regulated by the population densities. We propose and analyze the coupled system. We also apply our proposed scheme to three different models. Our results suggest that bi-directional migration makes the coupled system more regular. We have performed numerical simulations to illustrate the dynamics of the coupled systems.
Highlights
In mathematical biology, population theory plays an important role
Our aim of the present study is to investigate the role of migration on the stability of a coupled ecosystem for which one system shows chaotic dynamics, and the other system shows stable dynamics
We investigate the dynamics of the coupled ecosystem, for which one HP system shows chaotic dynamics and the other HP system shows stable dynamics
Summary
Population theory plays an important role. Historically, the first model of population dynamics was formulated by Malthus [1] and was later on adapted for more realistic situations by Verhulst [2]. Two systems can be coupled through migration, which is a common biological phenomenon and plays a vital role in the stability of ecosystems. Investigated the effect of bi-directional migration on the stability of two non-identical ecosystems, which were connected through migration. The above observations clearly indicate that migration has a major role in stabilizing chaotic ecosystems. The role of bi-directional migration for two similar types of ecosystems, where one is chaotic and the other is stable in nature, has not yet been investigated properly. We consider metapopulation dynamics of spatially separated food webs that are connected through bi-directional migrations. Our aim of the present study is to investigate the role of migration on the stability of a coupled ecosystem for which one system shows chaotic dynamics, and the other system shows stable dynamics.
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