The Impact of Immigration on a Stability Analysis of Lotka-Volterra System

Kaviya, R.; Muthukumar, P.

doi:10.1016/j.ifacol.2020.06.037

Cited by 5 publications

(3 citation statements)

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“…Also, the impact of immigration on the stability behavior of the LV system is analyzed. Our obtained results generalize the existing integer-order LV system with the immigration factor (see [ 18 – 24 ]).…”

Section: Introductionsupporting

confidence: 85%

“…In this work, we have provided evidence for the small changes of fractional orders that can provide a significant impact on the dynamic behavior of the LV system. In the literature, several valuable results such as stability analysis, persistence, permanence, and extinction are studied about the LV system (see [18][19][20][21][22][23][24][25][26][27][28][29]).…”

Section: Introductionmentioning

confidence: 99%

“…According to the migration on predator, the stability of the ecosystem will be changed. So that the immigration on predator has a vital role in the stability of prey-predator interactions (see [18][19][20][21][22][23][24]). By this importance of predator's immigration, we developed the fractional-order LV system with the predator immigration effect.…”

Section: Introductionmentioning

confidence: 99%

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Dynamical analysis and optimal harvesting of conformable fractional prey–predator system with predator immigration

Kaviya

Muthukumar

2021

Eur. Phys. J. Plus

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Aim of this work is to study the four species various fractional-order prey-predator or Lotka-Volterra (LV) system with both immigration and harvesting effects. The existence and uniqueness, uniform boundedness, persistence, permanence, and extinction of this system solution are analyzed. The stability behavior of the system is obtained with the help of the Routh-Hurwitz (RH) stability criterion. The small changes in fractional-order values can produce a significant impact on the stability of the system is confirmed. This work verifies that the small amount of immigration effect can change the dynamic nature of the LV system. Numerical results are given to illustrate the obtained theoretical results of the stability analysis. The bionomic equilibrium points of the system are attained with their feasibility conditions. To get the optimal amount of harvesting effect with the Pontryagin's maximum principle, the harvesting parameter is considered as the control parameter.

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Section: Introductionsupporting

confidence: 85%