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Study of A Predator-Prey Mathematical Model in a Bounded Area

Jane Mebri

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This Photo by Unknown Author is licensed under CC BY-NC-ND

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Introduction

  • Definition of Prey and Predator
  • Mathematical Model of Prey-Predator offered by Lotka and Volterra
  • Nonlinear Model of Prey-Predator with Boundary Conditions
  • Steady-State Equilibrium Solution
  • Numerical Solution
  • Conclusion

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Definition of Prey and Predator

PREDATOR

A predator is an organism that hunts, kills, and eats other organism to survive

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PREY

A prey is an organism that gets hunted and taken as food by other organism.

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Lotka-Volterra Model of �Prey-Predator

  •  

…(1)

…(2)

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Continued

  •  

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NONLINEAR MODEL OF PREY-PREDATOR EQUATIONS

 

…(3)

..(4)

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INITIAL CONDITIONS WITH BOUNDARY CONDITIONS

 

…(5)

…(6)

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Steady-State Equilibrium Solution

 

…(7)

…(8)

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Continued

 

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  •  

…(9)

…(10)

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Numerical Solutions

  •  

…..(11)

…..(12)

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Numerical Solutions

  •  
  •  

…..(13)

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Numerical Solutions

  •  

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Conclusion

  • The nonlinear Volterra model of prey and predator describes the reasons for fluctuations in predator and prey system, but it is impossible to describe the population change dynamics accurately because it is hard to estimate the value of all constants in the prey and predator equations (1) and (2).
  • When we found out that solution of u1=0 is stable from the steady-state equilibrium solution, then we observe that the smallest population in the studied model goes extinct at high preys’ mobility.
  • The total population depends on species’ mobility both of predators and preys.
  • The growth of predators’ mobility decreases the period of fluctuations and increases the preys’ number.

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Reference

  • Dynamic consequences of Lotka-Volterra predation model when the area ... (n.d.). Retrieved November 30, 2022, from https://www.researchgate.net/publication/282845289_Dynamic_consequences_of_Lotka-Volterra_predation_model_when_the_area_inhabited_by_the_preys_and_predators_decreases
  • A predator-prey mathematical model - ripublication.com. (n.d.). Retrieved November 30, 2022, from https://www.ripublication.com/gjpam16/gjpamv12n5_44.pdf
  • Redirecting. (n.d.). Retrieved November 30, 2022, from https://answers.microsoft.com/en-us/windows/forum/all/filecuserslynchdownloads14367rs1releaseclientprooe/c887b3c1-1a40-4926-b655-09abc901e841
  • Sandeep Kumar Follow. (n.d.). Lotka Volterra model. Share and Discover Knowledge on SlideShare. Retrieved November 30, 2022, from https://www.slideshare.net/SandeepKumar3250/lotka-volterra-model-157062109
  • Uva-Dare (Digital Academic Repository). (n.d.). Retrieved November 30, 2022, from https://pure.uva.nl/ws/files/2005181/27676_124811y.pdf

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Reference

  • Eugeny Petrovich Kolpak Saint Petersburg State University, Faculty of Applied Mathematics and Control Process, 199034, Saint Petersburg, Universitetskaya nab., 7/9, Russian Federation.
  • Mariia Vladimirovna Stolbovaia Saint Petersburg State University, Faculty of Applied Mathematics and Control Process, 199034, Saint Petersburg, Universitetskaya nab., 7/9, Russian Federation.
  • Inna Sergeevna Frantsuzova Saint Petersburg State University, Faculty of Applied Mathematics and Control Process, 199034, Saint Petersburg, Universitetskaya nab., 7/9, Russian Federation.