Role of competition in phytoplankton population for the occurrence and control of plankton bloom in the presence of environmental fluctuations

Stability of linear stochastic delay differential equations with infinite Markovian switchings

“…Considering the stochastic effects in models, such as influence due to thermal noise or intrinsic variations, stochastic delay differential equations (SDDEs) have attracted increasing interests in many different disciplines. An important area of application for the stability problem involving SDDEs is in biology and various other widespread topics can be found in previous works . Recently, there have appeared some works on the stabilities of SDDEs with the Markovian switchings, for instance, the works of Mao et al, Lan and Yuan, and Yuan et al However, all the works of Mao et al, Lan and Yuan, and Yuan et al focused on the case that the state spaces of the Markov chain are required to be finite.…”

“…An important area of application for the stability problem involving SDDEs is in biology and various other widespread topics can be found in previous works. [21][22][23][24][25][26][27] Recently, there have appeared some works on the stabilities of SDDEs with the Markovian switchings, for instance, the works of Mao et al, 28 Lan and Yuan, 29 and Yuan et al 30 However, all the works of Mao et al, 28 Lan and Yuan, 29 and Yuan et al 30 focused on the case that the state spaces of the Markov chain are required to be finite. As part of the results in the work of Mao et al, 28 the mean square exponential stability criteria of linear SDDE with Markovian switching were obtained.…”

Coexistence of competing predators in a coral reef ecosystem

“…In this section, we investigate numerically, as demonstrated in [21][22][23][24], the effect of the various parameters on the qualitative behavior of the system using parameter values given in Table 1 throughout, unless otherwise stated. We first observe that under the given set of parameter values the system approaches equilibrium at E * = (0.561, 0.2994, 0.0354, 0.192) in the form of a stable focus with eigenvalues −1.0376, −0.0312, 0.0492 ± i0.6862 (cf.…”

Effect of Dilution Rate on the Predictability of a Realistic Ecosystem Model With Instantaneous Nutrient Recycling

“…Recently role of competition in phytoplankton population for the occurrence and control of plankton bloom in the presence of environmental fluctuations and effect of toxin on NPZ model have been studied by Pal et al, 12,13 Bairagi et al 14 Effect of viral infection on nutrient-phytoplankton-zooplankton model has been studied by Chattopadhyay and Pal, 15 Chattopadhyay et al 16 The growth rates of both plankton populations are diminished when phytoplankton can uptake toxin in one model and in the other model zooplankton can uptake toxin have been discussed by Jang et al 17 Chakraborty and Chattopadhyay 18 discussed that the chance of extinction of population decreases due to additional food source even if in the presence of toxin released by phytoplankton. Ghosh 19 proposed and analyzed a nonlinear model for the biological control of algal bloom in a lake.…”