In this paper, the Allee effect is incorporated into a predator–prey model with linear functional response. Compared with the predator–prey model without the Allee effect, it is found that the Allee effect of the prey species increases the extinction risk of both the prey and predator. If...

We prove a Hopf bifurcation result for singular differential–algebraic equations (DAE) under the assumption that a trivial locus of equilibria is situated on the singularity as the bifurcation occurs. The structure that we need to obtain this result is that the linearisation of the DAE has a...

This paper describes a prey–predator model with Holling type II functional response incorporating prey refuge. The equilibria of the proposed system are determined and the behavior of the system is investigated around equilibria. Density-dependent mortality rate for the predator is considered...

Two time delays are assumed in a boundedly rational monopoly. The characteristic equation is derived for the general case, and a complete stability analysis is conducted both analytically and numerically in two special cases. In the first case, wherein the continuously distributed time delays...

A two dimensional two-delays differential system modeling the dynamics of stem-like cells and white-blood cells in Chronic Myelogenous Leukemia under treatment is considered. Stability of equilibria is investigated and emergence of periodic solutions of limit cycle type, as a result of a Hopf...

In this paper, a discrete predator–prey system is proposed and analyzed. It is assumed that the prey population has a lower critical point, which is also referred to as extinction threshold. Such behavior has been reported for many flowering plants, many fishes, epidemiology, and so on. The...

A continuous-time predator–prey model without spatial variation is proposed to study the impact of Allee effects upon the predator–prey interaction when the prey population is subject to Allee effects. The system exhibits a threshold below which both populations become extinct. The model...

The formation and growth of leaves around the stem of a plant often leads to a helical structure consisting of two counter-rotating sets of spirals. Similar arrangements (parastichies) are found for the petals, florets, stamens, etc. of many flowers. Douady and Couder [Phys. Rev. Lett. 68, 2098...

In the paper, the weather generator WGENK producing synthetic daily data of solar radiation, maximum and minimum temperature, and total precipitation is presented. A WGENK model, modification of WGEN model, introduces annual courses of transition probability, α parameter of Γ distribution, and...