Lotka–Volterra Model Predator–prey Systems Polynomial (P)–type Control Numerical Simulations Murray’s Reaction Differential System
Academic Publications, Ltd.
Kyurkchiev, N., Boyadjiev, G.. Dynamics of Modified Lotka-Volterra Model with Polynomial Intervention Factors. Methodological Aspects. III. lnternational Journal of Differential Equations and Applications, 20, 1, 2021, DOI:10.12732/ijdea.v20i1.9, 121-132.
lnternational Journal of Differential Equations and Applications;20(1)
In the present article is considered a modification of the classical Lotka–Volterra model. The ’input functions α(t) and γ(t) are algebraic polynomials of degree n, α(t) is monotonically increasing (with ”saturation”) and γ(t) > 0 is monotonically decreasing in the considered interval. This model is very sensitive with respect to the coefficients of the polynomials a_i and b_i. Therefore it is attractive for conducting computer simulations, including other modified predator-prey models and activator-inhibitor mechanisms. Numerical examples, illustrating our results are given using CAS Mathematica.