Effects of supplying alternative food in a predator–prey model with harvesting

Dynamical Analysis of Fractional-Order Hastings-Powell Food Chain Model with Alternative Food

“…The model construction is done by modifying the model of Sahoo and Poria [2] by changing the integer order into the fractional-order.…”

“…However, alternative prey (supplementary feeding) for top-predators can reduce predation rates in intermediate-predators [2], then to give this effect, model (1) can be modified to…”

“…Mathematical model used to describe interactions between predator and prey is called the predator-prey model. Furthermore, many interesting fenomena in ecology can be described by mathematical model through predator-prey models such as harvesting in predator population [1], supplying alternative food in a predator population [2], refuging prey population [3], spreading disease in ecosystem [4], and the effect of the present an omnivore [5]. In predator prey model [2], it is assumed that prey populations do not always exist, they also experience migration to find new habitats due to climate change factors and low food reserves.…”

Stability and Hopf bifurcation for a stage-structured predator–prey model incorporating refuge for prey and additional food for predator

“…In fact, additional food is an important component of most predators. Recently, the effects of the additional food to predator in prey-predator models were investigated [14][15][16][17][18][19]. Srinivasu et al [14] reported the dynamics of prey-predator system in the presence of additional food for predator and discussed the effect of quality and quantity of the additional food.…”

Global asymptotical stability of almost periodic solutions for a non-autonomous competing model with time-varying delays and feedback controls

“…For example, Sarwardi et al [27] focused on the local and the global stability and the bifurcations of a competitive preypredator system with a prey refuge, Ko and Ahn [16] discussed the global attractor, persistence and the stability of all non-negative equilibria of a diffusive one-prey and two-competing-predator system with a ratio-dependent functional response, Pan et al [25] considered Gause , s principle in interspecific competition of the cyclic predatorprey system, Qun Liu et al [23] addressed the global stability of a stochastic predatorprey system with infinite delays. For more related works on this topic, one can see [2,3,6,[9][10][11][12]14,15,18,20,24,26,28,29,31,34,35,38]. In 2001, Zhang et al [36] investigated the permanence of the following non-autonomous competing model dx 1 (t)…”