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Persistence and Extinction of One-Prey and Two-Predators System
In this paper, a mathematical model is proposed and analysed to study the dynamics of one-prey two-predators system with ratio-dependent pre- dators growth rate. Criteria for local stability,Expand
Why chaos is rarely observed in natural populations
Abstract An attempt has been made to understand why chaotic dynamics have received poor evidential support from field studies. Our study opens up the possibility that the cause of failure might notExpand
Multiple attractors and crisis route to chaos in a model food-chain
Abstract An attempt has been made to identify the mechanism, which is responsible for the existence of chaos in narrow parameter range in a realistic ecological model food-chain. Analytical andExpand
Dynamics of generalist predator in a stochastic environment: Effect of delayed growth and prey refuge
TLDR
It is observed that delay destabilizes the system, in general and stability loss occurs via Hopf-bifurcation, and it is shown that there exists critical values of the delay parameters below which the coexistence equilibrium is stable and above which it is unstable. Expand
Dynamics of a three species food chain model with Crowley–Martin type functional response
Abstract In this paper, a three species food chain model, consisting of a hybrid type of prey-dependent and predator-dependent functional responses, is investigated analytically as well asExpand
Chaos to Order: Role of Toxin Producing Phytoplankton in Aquatic Systems
TLDR
It is observed that the strength of toxic substance change the state from chaos to order and TPP has a stabilizing contribution in aquatic systems and may be used as a bio-control mechanism. Expand
Complex dynamics of a three species food-chain model with Holling type IV functional response
In this paper, dynamical complexities of a three species food chain model with Holling type IV predator response is investigated analytically as well as numerically. The local and global stabilityExpand
Dynamical Complexity in Some Ecological Models: Effect of Toxin Production by Phytoplankton
TLDR
The study shows that chaotic dynamics is robust to changes in the rates of toxin release as well as the toxin release functions, and reveals that the rate of toxin p roduction by toxin producing phytoplankton plays an important role in controlling oscillation s in the plankton system. Expand
Chaos: An Ecological Reality?
TLDR
A new methodology for the analysis of a class of model ecological systems is presented and it is pointed out that the failure of attempts to observe chaos in natural populations might have resulted because biological interactions are not conducive for such a behavior to be supported. Expand
Fractional-order leaky integrate-and-fire model with long-term memory and power law dynamics
TLDR
The results suggest that fractional-order models might be appropriate for understanding multiple time scale neuronal dynamics, and a neuron with fractional dynamics displays history dependent activities that might be very useful and powerful for effective information processing. Expand
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