Abstract
In prey-predator system prey populations take various defensive mechanism to save themselves from predator and/or to get advantage in inter-species competition. In this work, we analyzed the dynamics of prey- predator system with two prey species and single predator population in which two prey populations are fighting for the same resources. Here, it is assumed that one prey population exhibits herd behavior as their own defense mechanism and second prey population releases toxin elements which gives them advantage of inter-species com- petition. From the analysis of our model we observed that the strategy of herd behavior as self defense mechanism is stronger than the toxin producing strategy. Also due to herd behavior of prey the model shows ecologically meaningful dynamics near origin.
Highlights
Ecosystems are characterized by the interaction between different species and natural environment
We analyze the dynamics of prey-predator system with two prey species and single predator population in which two prey populations are fighting for the same resources and the first prey population exhibits herd behavior
We are interested to analyze the dynamics of prey-predator system with two prey species and single predator population in which two prey populations are fighting for the same resources
Summary
Ecosystems are characterized by the interaction between different species and natural environment. As a mathematical consequence of the herd behavior, they considered competition models and predator-prey systems in which interaction terms use the square root of the prey population rather than the prey population. Chattopadhyay et al and Coauthors [25] recognized that certain plankton (prey) aggregate in large groups so that the predator effectively only has access to them by way of surface area instead of volume As demonstrated by these authors, using appropriate powers of the variables to properly account for the way of predators and prey aggregate is an innovation that allows for a more realistic portrayal of certain predator-prey systems. This type of advance is somewhat typical in the history of the development of predator-prey models. We analyze the dynamics of prey-predator system with two prey species and single predator population in which two prey populations are fighting for the same resources and the first prey population exhibits herd behavior
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