Top-predator interference and gestation delay as determinants of the dynamics of a realistic model food chain

Predator interference effects on biological control: The “paradox” of the generalist predator revisited

“…Upadhyay and Agrawal [55] investigated the effect of mutual interference on the dynamics of delay induced predator prey system, and determined the conditions under which the model becomes globally asymptotically stable around the nonzero equilibria. Recently, Jana et al [56] have made an attempt to understand the role of top predator interference and gestation delay on the dynamics of a three species food chain model. Interaction between the prey and the middle predator follows Volterra scheme, while that between the top predator and its prey depends on the Beddington-DeAngelis type functional response.…”

Photosynthesis rate, salinity induced grazing rate and gestation delay as determinants of the dynamics of a realistic food chain model: a stochastic approach

“…On a fairly realistic ecological model with generalist top predator, Upadhyay et al (2007) investigate the influence of environmental noise and show the importance of the noise amplitude on the trophic level and the susceptibility of populations to environmental noise. Complex dynamical behavior of a biological system arises as a consequence of time delay (with significant time delay) which may exhibit limit cycle oscillations (Ruan 2009) and chaos (Mackey and Glass 1977;Jana 2014;Jana et al 2014). In reality, time delays occur in almost every ecological situation and assume to be one of the most prominent reason of regular fluctuations on population biomass (Jana 2014;Jana et al 2014Jana et al , 2015.…”

“…Complex dynamical behavior of a biological system arises as a consequence of time delay (with significant time delay) which may exhibit limit cycle oscillations (Ruan 2009) and chaos (Mackey and Glass 1977;Jana 2014;Jana et al 2014). In reality, time delays occur in almost every ecological situation and assume to be one of the most prominent reason of regular fluctuations on population biomass (Jana 2014;Jana et al 2014Jana et al , 2015. Ruan (2009) presents a brief review on prey-predator models with descrete delay for both Kolmogorov and non-Kolmogorov type model system.…”

“…It often represents gestation time (Jana 2014;Jana et al 2014), incubation period, transport delay or can simply lump complicated biological process together, accounting only for the time requires for these process to occur. Delay parameter emphasizes on Hopf-bifurcation (Ruan 2009;Jana 2014;Jana et al 2014Jana et al , 2015 and also it causes some complex dynamical behaviors, such as double Hopf bifurcation, quasi-periodic solutions and chaos (Lü 2002;Ma et al 2008;Matouk 2008;Ding and Jiang 2011;Wang et al 2014;Ding et al 2013;Song and Xu 2013). Along with different studies of environmental stochasticity and biological delays in prey-predator system, influence of noise on a delayed system is very significant for advance study of biological system.…”

Global Stability and Hopf-bifurcation Analysis of Biological Systems using Delayed Extended Rosenzweig-MacArthur Model

“…Also, the dynamical behaviors of such systems including global stability, instability, Hopf-bifurcations, strange chaotic attractor are induced by delayed parameters. (see, Feng & Hongwei, 2012;Wang & Li 2003;Xu & Wu, 2014;Agrawal, Jana & Upadhyay, 2014;Jatav & Dhar, 2015). Thus, more realistic mathematical models in ecological population dynamics needs to incorporate a time lag or history between the moment in which an action takes place and the moment its effect is actually observed in the dynamical system.…”