Dynamics of generalist predator in a stochastic environment: Effect of delayed growth and prey refuge

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

“…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.…”

“…Understanding the dynamical relationship between prey and predator through mathematical modelling in theoretical ecology has gained a lot of importance during the last few decades (Berryman 1992). On the purpose of observation and study the effect of environmental noise on population dynamics, researchers have used Gaussian white-noise (Lande 1993;May 1973;Jana et al 2015) and color noise (Samanta and Maiti 2003;Jana and Bairagi 2013) as a model of environmental variations. May (1973) studies a population model considering white noise and shows that when the population deviates more from equilibrium point, the system shows irregular behavior (i.e., instability).…”

“…May (1973) studies a population model considering white noise and shows that when the population deviates more from equilibrium point, the system shows irregular behavior (i.e., instability). Where as Jana et al (2015) show a three species food chain model where the interacting processes among the species are influenced by Gaussian white-noise and with increasing noise intensity system gradually goes into chaos from stable coexistence through instability stochastically. Ripa et al (1998) examine the effect of environmental noise on population and present a general theory of environmental noise in ecological food webs.…”

Temperature dependent growth rate of phytoplankton and salinity induced grazing rate of zooplankton as determinants of realistic multi-delayed food chain model

“…Jana and Samanta (2014) show the complex dynamical results of a multi-delayed ratio-dependent prey-predator system with prey harvesting under stochastic environment. Where as Jana et al (2015) show the effect of multiple delays on the dynamics of generalist predator in a stochastic environment. Effect of age-selective harvesting of both prey and predator is studied by Jana et al (2016).…”

“…Models with delay are much more realistic. In reality time delays occur in almost every biological situation (Jana et al 2015;MacDonald 1989;) and assumed to be one of the significant reasons of regular fluctuations in population density (Jana et al 2015;MacDonald 1989;May 1981). Reproduction of predator after consuming prey is not instantaneous, but mediated by some time lag required for gestation.…”