In this paper, a mathematical model consisting of the prey- predator model with treatment and disease infection in prey population is proposed and analyzed. The existence, uniqueness and boundedness of the solution are discussed. The stability analyses of all possible equilibrium points are studied. Numerical simulation is carried out to investigate the global dynamical behavior of the system.

In this paper,  a Sokol-Howell prey-predator model involving strong Allee effect is proposed and analyzed. The existence, uniqueness, and boundedness are studied. All the five possible equilibria have been are obtained and their local stability conditions are established. Using Sotomayor's theorem, the conditions of local saddle-node and transcritical and pitchfork bifurcation are derived and drawn. Numerical simulations are performed to clarify the analytical results

The avoidance strategy of prey to predation and the predation strategy for predators are important topics in evolutionary biology. Both prey and predators adjust their behaviors in order to obtain the maximal benefits and to raise their biomass for each. Therefore, this paper is aimed at studying the impact of prey’s fear and group defense against predation on the dynamics of the food-web model. Consequently, in this paper, a mathematical model that describes a tritrophic Leslie-Gower food-web system is formulated. Sokol-Howell type of function response is adapted to describe the predation process due to the prey’s group defensive capability. The effects of fear due to the predation process are considered in the first two levels

       This paper treats the interactions among four population species. The system includes one mutuality prey, one harvested prey and two predators. The four species interaction can be described as a food chain, where the first prey helps the second harvested prey. The first and the second predator attack the first and the second prey, respectively, according to Lotka-Volterra type functional responses. The model is formulated using differential equations. One equilibrium point of the model is found and analysed to reveal a threshold that will allow the coexistence of all species. All other equilibrium points of the system are located, with their local and global stability being assessed. To back up the conclusions of the mathema

The appearance of Mixed Mode Oscillations (MMOs) and chaotic spiking in a Light Emitting Diode (LED) with optoelectronic feedback theoretically and experimentally have been reported. The transition between periodic and chaotic mixed-mode states has been investigated by varying feedback strength. In incoherent semiconductor chaotically spiking attractors with optoelectronic feedback have been observed to be the result of canard phenomena in three-dimensional phase space (incomplete homoclinic scenarios).

In this paper, a discrete- time ratio-dependent prey- predator model is proposed and analyzed. All possible fixed points have been obtained. The local stability conditions for these fixed points have been established. The global stability of the proposed system is investigated numerically. Bifurcation diagrams as a function of growth rate of the prey species are drawn. It is observed that the proposed system has rich dynamics including chaos.