DYNAMICS OF MODIFIED LOTKA–VOLTERRA MODEL WITH POLYNOMIAL INTERVENTION FACTORS. METHODOLOGICAL ASPECTS. III

Abstract

In the present article is considered a modification of the classicalLotka–Volterra model. The ’input functions alpha(t) and gamma(t) are algebraic polynomi-als of degree n, alpha(t) is monotonically increasing (with ”saturation”) and gamma(t) > 0 ismonotonically decreasing in the considered interval. This model is very sensitive withrespect to the coefficients of the polynomials ai and bi. Therefore it is attractive forconducting computer simulations, including other modified predator-prey models andactivator-inhibitor mechanisms.

Numerical examples, illustrating our results are givenusing CAS Mathematica.