Effects of seasonal growth on ratio dependent delayed prey predator system

A delayed ratio-dependent predator-prey system with stage-structured and impulsive effect

“…This roughly states that the per capita predator growth rate should be a function of the ratio of prey to predator abundance. This is strongly supported by numerous fields and laboratory experiments and observations [13−16] , and ratio-dependent delayed predator-prey model has been well studied (for example, [17]). …”

Rich dynamic of a stage-structured prey–predator model with cannibalism and periodic attacking rate

“…From the conditions ðH 3 Þ and ðH 5 Þ, we get 3) also can be considered as a continuous forced system. This type of systems have been extensively studied by many authors [22][23][24][25] and they found that the periodic external force play an important role on these systems, which maybe induce many complex dynamical behaviors even including chaos.…”

“…Motivated by the works [22][23][24][25], where the population communities are imbedded in seasonally forced environments and the effect of seasonality is looked on as sinusoidal perturbation on the original intrinsic growth rate of prey, we select a 1 ðtÞ and a 2 ðtÞ in the forms of a 1 ðtÞ ¼ a 1 ð1 þ e sinðxtÞÞ; a 2 ðtÞ ¼ a 2 ð1 þ e sinðxtÞÞ. The parameter a 1 is the average value of a 1 ðtÞ and e is the starvation degree; a 1 e is the magnitude of the perturbation and x is the angular frequency of the fluctuation caused by starvation.…”

Stability and Bifurcation Analysis in a Maglev System with Multiple Delays

“…Many authors have discussed dynamical models with multiple delays [Bélair & Campbell, 1994;Gakkhar et al, 2009a;Guo et al, 2008;Huang et al, 2007;Sunita & Anuraj, 2012;Yuan & Song, 2009]. Bélair and Campbell [1994] found that a double Hopf bifurcation would occur in a first-order delay differential system when two different network delay feedback effects are considered, and this work resulted in creating a double Hopf bifurcation with two time-delays research.…”