A systematic study of autonomous and nonautonomous predator–prey models for the combined effects of fear, refuge, cooperation and harvesting

In the present study, we investigate the roles of fear, refuge and hunting cooperation on the dynamics of a predator–prey system, where the predator population is subject to harvesting at a nonlinear rate. We also focus on the effects of seasonal forcing by letting some of the model parameters to va...

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Published in:European physical journal plus Vol. 137; no. 6; p. 724
Main Authors: Mondal, Bapin, Roy, Subarna, Ghosh, Uttam, Tiwari, Pankaj Kumar
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 22.06.2022
Springer Nature B.V
Subjects:
Applied and Technical Physics
Atomic
Birth rate
Complex Systems
Condensed Matter Physics
Cooperation
Ecosystems
Endangered & extinct species
Fear
Food
Hunting
Mathematical and Computational Physics
Mathematical models
Molecular
Optical and Plasma Physics
Parameters
Physics
Physics and Astronomy
Predation
Predator-prey simulation
Predators
Prey
Regular
Regular Article
Theoretical
ISSN:2190-5444, 2190-5444
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Abstract In the present study, we investigate the roles of fear, refuge and hunting cooperation on the dynamics of a predator–prey system, where the predator population is subject to harvesting at a nonlinear rate. We also focus on the effects of seasonal forcing by letting some of the model parameters to vary with time. We rigorously analyze the autonomous and nonautonomous models mathematically as well as numerically. Our simulation results show that the birth rate of prey and the fear of predators causing decline in it, and harvesting of predators first destabilize and then stabilize the system around the coexistence of prey and predator; if the birth rate of prey is very low, both prey and predator populations extinct from the ecosystem, and for a range of this parameter, only the prey population survive. The fear of predators responsible for increase in the intraspecific competition among the prey species and the refuge behavior of prey have tendency to stabilize the system, whereas the cooperative behavior of predators during the hunting time destroys stability in the ecosystem. Numerical investigations of the seasonally forced model showcase the appearances of periodic solution, higher periodic solutions, bursting patterns and chaotic dynamics.
AbstractList In the present study, we investigate the roles of fear, refuge and hunting cooperation on the dynamics of a predator–prey system, where the predator population is subject to harvesting at a nonlinear rate. We also focus on the effects of seasonal forcing by letting some of the model parameters to vary with time. We rigorously analyze the autonomous and nonautonomous models mathematically as well as numerically. Our simulation results show that the birth rate of prey and the fear of predators causing decline in it, and harvesting of predators first destabilize and then stabilize the system around the coexistence of prey and predator; if the birth rate of prey is very low, both prey and predator populations extinct from the ecosystem, and for a range of this parameter, only the prey population survive. The fear of predators responsible for increase in the intraspecific competition among the prey species and the refuge behavior of prey have tendency to stabilize the system, whereas the cooperative behavior of predators during the hunting time destroys stability in the ecosystem. Numerical investigations of the seasonally forced model showcase the appearances of periodic solution, higher periodic solutions, bursting patterns and chaotic dynamics.
In the present study, we investigate the roles of fear, refuge and hunting cooperation on the dynamics of a predator-prey system, where the predator population is subject to harvesting at a nonlinear rate. We also focus on the effects of seasonal forcing by letting some of the model parameters to vary with time. We rigorously analyze the autonomous and nonautonomous models mathematically as well as numerically. Our simulation results show that the birth rate of prey and the fear of predators causing decline in it, and harvesting of predators first destabilize and then stabilize the system around the coexistence of prey and predator; if the birth rate of prey is very low, both prey and predator populations extinct from the ecosystem, and for a range of this parameter, only the prey population survive. The fear of predators responsible for increase in the intraspecific competition among the prey species and the refuge behavior of prey have tendency to stabilize the system, whereas the cooperative behavior of predators during the hunting time destroys stability in the ecosystem. Numerical investigations of the seasonally forced model showcase the appearances of periodic solution, higher periodic solutions, bursting patterns and chaotic dynamics.In the present study, we investigate the roles of fear, refuge and hunting cooperation on the dynamics of a predator-prey system, where the predator population is subject to harvesting at a nonlinear rate. We also focus on the effects of seasonal forcing by letting some of the model parameters to vary with time. We rigorously analyze the autonomous and nonautonomous models mathematically as well as numerically. Our simulation results show that the birth rate of prey and the fear of predators causing decline in it, and harvesting of predators first destabilize and then stabilize the system around the coexistence of prey and predator; if the birth rate of prey is very low, both prey and predator populations extinct from the ecosystem, and for a range of this parameter, only the prey population survive. The fear of predators responsible for increase in the intraspecific competition among the prey species and the refuge behavior of prey have tendency to stabilize the system, whereas the cooperative behavior of predators during the hunting time destroys stability in the ecosystem. Numerical investigations of the seasonally forced model showcase the appearances of periodic solution, higher periodic solutions, bursting patterns and chaotic dynamics.
ArticleNumber 724
Author Mondal, Bapin
Roy, Subarna
Ghosh, Uttam
Tiwari, Pankaj Kumar
Author_xml – sequence: 1
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  fullname: Mondal, Bapin
  organization: Department of Applied Mathematics, University of Calcutta
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  fullname: Roy, Subarna
  organization: Department of Basic Science and Humanities, Indian Institute of Information Technology
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  givenname: Uttam
  surname: Ghosh
  fullname: Ghosh, Uttam
  organization: Department of Applied Mathematics, University of Calcutta
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  givenname: Pankaj Kumar
  surname: Tiwari
  fullname: Tiwari, Pankaj Kumar
  email: pktiwari.math@iiitbh.ac.in
  organization: Department of Basic Science and Humanities, Indian Institute of Information Technology
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The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022.
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Snippet In the present study, we investigate the roles of fear, refuge and hunting cooperation on the dynamics of a predator–prey system, where the predator population...
In the present study, we investigate the roles of fear, refuge and hunting cooperation on the dynamics of a predator-prey system, where the predator population...
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SubjectTerms Applied and Technical Physics
Atomic
Birth rate
Complex Systems
Condensed Matter Physics
Cooperation
Ecosystems
Endangered & extinct species
Fear
Food
Hunting
Mathematical and Computational Physics
Mathematical models
Molecular
Optical and Plasma Physics
Parameters
Physics
Physics and Astronomy
Predation
Predator-prey simulation
Predators
Prey
Regular
Regular Article
Theoretical
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Title A systematic study of autonomous and nonautonomous predator–prey models for the combined effects of fear, refuge, cooperation and harvesting
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