arXiv subjects

Debaldev Jana

Publications and source records attributed to Debaldev Jana.

5 recordsLinked to original sources

arXiv2026

Effect of wind on prey-predator dynamics with group defense and additional food strategy

Wind plays a crucial role in changing prey defense strategy and predation efficiency. We develop and analyze a prey-predator model that incorporates wind driven environmental effects, prey group defense, and an additional food strategy for the predator. Wind intensity is assumed to modulate predation efficiency, while prey aggregation reduces predation pressure at high densities, and supplementary food alters predator growth independent of prey abundance. We investigate the existence and stability of biologically feasible equilibrium points. The analysis reveals that wind strength and additional food supply can induce stability switches, oscillatory dynamics via Hopf bifurcation, and more complex behaviors including saddle node and Bogdanov Takens bifurcations. Our results demonstrate that environmental forcing and resource supplementation jointly shape predator persistence and population fluctuations, providing theoretical insights into ecological management strategies involving food enrichment under variable environmental conditions.

q-bio.PE↗

arXiv2020

Self-diffusion Driven Pattern Formation in Prey-Predator System with Complex Habitat under Fear Effect

In the present work, we explore the influence of habitat complexity on the activities of prey and predator of a spatio-temporal system by incorporating self diffusion. First we modify the Rosenzweig-MacArthur predator-prey model by incorporating the effects of habitat complexity on the carrying capacity and fear effect of prey and predator functional response. We establish conditions for the existence and stability of all feasible equilibrium points of the non-spatial model and later we prove the existence of Hopf and transcritical bifurcations in different parametric phase-planes analytically and numerically. The stability of the spatial system is studied and we discuss the conditions for Turing instability. Selecting suitable control parameter from the Turing space, the existence conditions for stable patterns are derived using the amplitude equations. Results obtained from theoretical analysis of the amplitude equations are justified by numerical simulation results near the critical parameter value. Further, from numerical simulation, we illustrate the effect of diffusion of the dynamical system in the spatial domain by different pattern formations. Thus our model clearly shows that the fear effect of prey and predator's functional response make an anti-predator behaviour including habitat complexity which helps the prey to survive in the spatio-temporal domain through diffusive process.

nlin.PS↗

arXiv2020

Dynamics of a non-autonomous system with age-structured growth and harvesting of prey and mutually interfering predator with reliance on alternative food

We perform a detailed analysis of the behaviour of a non-autonomous prey-predator model where age based growth with age discriminatory harvesting in prey and predator's reliance upon alternative food in the absence of that particular prey are considered. We begin by deriving certain sufficient conditions for permanence and positive invariance and then proceed to construct a Lyapunov function to derive some constraints for global attractivity. With the help of continuation theorem we arrive at the best fit criterion to prove the occurrence of a positive periodic solution. Moreover, using Arzela-Ascoli theorem we formulate a proof for a unique positive solution to be almost periodic and we carry out numerical simulation to verify the analytical findings. With the aid of graphs and tables we show the nature of the prey-predator system in response to the alternative food and delays.

q-bio.PE↗

arXiv2020

Interplay between reproduction and age selective harvesting delays of a single population non-autonomous system

This paper is concerned with an analysis of the dynamics of a non-autonomous, single population age based growth model with harvesting formulation. First, we derive sufficient conditions for permanence and positive invariance. Then, by constructing a scalar function, namely the Lyapunov function, we arrive at a suitable criterion for global attractivity. With the help of Brouwer fixed point and continuation theorems, we obtain constraints for the existence of a positive periodic solution. Then we prove that there exists only one solution which is almost periodic in nature that is distinct from every other solution. Further, we carry out a numerical simulation to support the analytical findings.

q-bio.PE↗

arXiv2016

Complex dynamics generated by negative and positive feedback delays of a prey-predator system with prey refuge: Hopf bifurcation to Chaos

Various field and laboratory experiments show that prey refuge plays a significant role in the stability of prey-predator dynamics. On the other hand, theoretical studies show that delayed system exhibits a much more realistic dynamics than its non-delayed counterpart. In this paper, we study a multi-delayed prey-predator model with prey refuge. We consider modified Holling Type II response function that incorporates the effect of prey refuge and then introduce two discrete delays in the model system. A negative feedback delay is considered in the logistic prey growth rate to represent density dependent feedback mechanism and a positive feedback delay is considered to represent the gestation time of the predator. Our study reveals that the system exhibits different dynamical behaviors, viz., stable coexistence, periodic coexistence or chaos depending on the values of the delay parameters and degree of prey refuge. The interplay between two delays for a fixed value of prey refuge has also been determined. It is noticed that these delays work in a complementary fashion. In addition, using the normal form theory and center manifold argument, we derive the explicit formulae for determining the direction of the bifurcation, the stability and other properties of the bifurcating periodic solutions.

math.DS↗