Razie Shafeii Lashkarian
Department of Basic science, Hashtgerd Branch, Islamic Azad University, Alborz, Iran
[ 1 ] - Discretization of a fractional order ratio-dependent functional response predator-prey model, bifurcation and chaos
This paper deals with a ratio-dependent functional response predator-prey model with a fractional order derivative. The ratio-dependent models are very interesting, since they expose neither the paradox of enrichment nor the biological control paradox. We study the local stability of equilibria of the original system and its discretized counterpart. We show that the discretized system, which is...
[ 2 ] - Some new families of definite polynomials and the composition conjectures
The planar polynomial vector fields with a center at the origin can be written as an scalar differential equation, for example Abel equation. If the coefficients of an Abel equation satisfy the composition condition, then the Abel equation has a center at the origin. Also the composition condition is sufficient for vanishing the first order moments of the coefficients. The composition conjectur...
[ 3 ] - Threshold harvesting policy and delayed ratio-dependent functional response predator-prey model
This paper deals with a delayed ratio-dependent functional response predator-prey model with a threshold harvesting policy. We study the equilibria of the system before and after the threshold. We show that the threshold harvesting can improve the undesirable behavior such as nonexistence of interior equilibria. The global analysis of the model as well as boundedness and permanence properties a...
[ 4 ] - Monodromy problem for the degenerate critical points
For the polynomial planar vector fields with a hyperbolic or nilpotent critical point at the origin, the monodromy problem has been solved, but for the strongly degenerate critical points this problem is still open. When the critical point is monodromic, the stability problem or the center- focus problem is an open problem too. In this paper we will consider the polynomial planar vector fields ...
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