arXiv subjects

Nandadulal Bairagi

Publications and source records attributed to Nandadulal Bairagi.

10 recordsLinked to original sources

arXiv2024

On the stability of fractional order Leslie-Gower type model with non-monotone functional response of intermediate predator

In this paper, an attempt is made to understand the dynamics of a fractional order three species Leslie-Gower predator prey food chain model with simplified Holling type IV functional response by considering fractional derivative in Caputo Sense. First, we prove different mathematical results like existence, uniqueness, non-negativity and boundedness of the solutions of fractional order dynamical system. The dissipativeness of the solution of the FDE system is discussed. Further, we investigate the Local stability criteria of all feasible equilibrium points. Global stability of the interior equilibrium point have also been discussed here. Using realistic parameter values, numerically it has been observed that the fractional order system shows more complex dynamics, like chaos as fractional order becomes larger. Analytical results are illustrated with several examples in numerical section.

math.DS↗

arXiv2022

Multimodal distribution of transient time of predator extinction in a three-species food chain

Studies of transient dynamics captures the time history of any dramatic changes in the dynamics of a system. The transient dynamics is investigated here in a classic ecological model of a bistable tri-trophic food chain. All the species in the food chain either coexist or undergoes a partial extinction with the loss of predator after a transient time that depends upon the initial density of species populations. The distribution of transient time of extinction of the predator in response to initial states shows interesting pattern of inhomogeneity and anisotropy in the basin of predator-fee state. Precisely, the distribution shows a multimodal character when the initial points are near the basin boundary, and unimodal at locations far from the border. The distribution is also anisotropic in the sense that the number of modes depends on the direction from the basin location. We define two new metrics, viz., homogeneity index and local isotropic index to characterize the distinctive features of the distribution. The inhomogeneity of distribution reduces significantly with resource enrichment, however, a similar change in anisotropy is relatively low. We try to explain the origin of such multimodal distributions from the dynamical system perspectives and present its ecological implications.

q-bio.PE↗

arXiv2021

Study of a Discretized Fractional-order eco-epidemiological model with prey infection

In this paper, an attempt is made to understand the dynamics of a three-dimensional discrete fractional-order eco-epidemiological model with Holling type II functional response. We first discretize a fractional-order predator-prey-parasite system with piecewise constant arguments and then explore the system dynamics. Analytical conditions for the local stability of different fixed points have been determined using the Jury criterion. Several examples are given to substantiate the analytical results. Our analysis shows that stability of the discrete fractional order system strongly depends on the step-size and the fractional order. More specifically, the critical value of the step-size, where the switching of stability occurs, decreases as the order of the fractional derivative decreases. Simulation results explore that the discrete fractional-order system may also exhibit complex dynamics, like chaos, for higher step-size.

math.DS↗

arXiv2020

Infection spreading and recovery in a square lattice

We investigate spreading and recovery of disease in a square lattice, and in particular, emphasize the role of the initial distribution of infected patches in the network, on the progression of an endemic and initiation of a recovery process, if any, due to migration of both the susceptible and infected hosts. The disease starts in the lattice with three possible initial distribution patterns of infected and infection-free sites, infected core patches (ICP), infected peripheral patches (IPP) and randomly distributed infected patches (RDIP). Our results show that infection spreads monotonically in the lattice with increasing migration without showing any sign of recovery in the ICP case. In the IPP case, it follows a similar monotonic progression with increasing migration, however, a self-organized healing process starts for higher migration, leading the lattice to full recovery at a critical rate of migration. Encouragingly, for the initial RDIP arrangement, chances of recovery are much higher with a lower rate of critical migration. An eigenvalue based semi-analytical study is made to determine the critical migration rate for realizing a stable infection-free lattice. The initial fraction of infected patches and the force of infection play significant roles in the self-organized recovery. They follow an exponential law, for the RDIP case, that governs the recovery process. For the frustrating case of ICP arrangement, we propose a random rewiring of links in the lattice allowing long-distance migratory paths that effectively initiate a recovery process. Global prevalence of infection thereby declines and progressively improves with the rewiring probability that follows a power law with the critical migration and leads to the birth of emergent infection-free networks.

q-bio.PE↗

arXiv2019

Dynamics of vertically and horizontally transmitted parasites: Continuous vs Discrete Models

In this paper we analyze a continuous-time epidemic model and its discrete counterpart, where infection spreads both horizontally and vertically. We consider three cases: model with horizontal and imperfect vertical transmissions, model with horizontal and perfect vertical transmissions, and model with perfect vertical and no horizontal transmissions. Stability of different equilibrium points of both the continuous and discrete systems in all cases are determined. It is shown that the stability criteria are identical for continuous and discrete systems. The dynamics of the discrete system have also shown to be independent of the step-size. Numerical computations are presented to illustrate analytical results of both the systems and their subsystems.

math.DS↗

arXiv2019

On the Dynamic Consistency of a Discrete Predator-Prey Model

We here discretize a predator-prey model by standard Euler forward method and non-standard finite difference method and then compare their dynamic properties with the corresponding continuous-time model. We show that NSFD model preserves positivity of solutions and is completely consistent with the dynamics of the corresponding continuous-time model. On the other hand, the discrete model formulated by forward Euler method does not show dynamic consistency with its continuous counterpart. Rather it shows scheme--dependent instability when step--size restriction is violated.

math.DS↗

arXiv2019

A fractional calculus approach to Rosenzweig-MacArthur predator-prey model and its solution

In this paper we present analytical solution of a fractional order predator-prey model, where prey grows logistically and predation occurs following type II response function, by homotopy perturbation method. Numerical solutions are presented to illustrate different particular cases. Our computational results show that accurate solution may be obtained with few iterations.

math.DS↗

arXiv2019

Local and global dynamics of a fractional-order predator-prey system with habitat complexity and the corresponding discretized fractional-order system

This paper is focused on local and global stability of a fractional-order predator-prey model with habitat complexity constructed in the Caputo sense and corresponding discrete fractional-order system. Mathematical results like positivity and boundedness of the solutions in fractional-order model is presented. Conditions for local and global stability of different equilibrium points are proved. It is shown that there may exist fractional-order-dependent instability through Hopf bifurcation for both fractional-order and corresponding discrete systems. Dynamics of the discrete fractional-order model is more complex and depends on both step length and fractional-order. It shows Hopf bifurcation, flip bifurcation and more complex dynamics with respect to the step size. Several examples are presented to substantiate the analytical results.

math.DS↗

arXiv2019

Analysis of a fractional order eco-epidemiological model with prey infection and type II functional response

In this paper, we introduce fractional order into an ecoepidemiological model, where predator consumes disproportionately large number of infected preys following type II response function. We prove different mathematical results like existence, uniqueness, non-negativity and boundedness of the solutions of fractional order system. We also prove the local and global stability of different equilibrium points of the system. The results are illustrated with several examples.

math.DS↗

arXiv2019

Global stability of a Leslie-Gower-type fractional order tritrophic food chain model

Recently, the dynamical behaviors of a fractional order three species food chain model was studied by Alidousti and Ghahfarokhi ({\it Nonlinear Dynamics, doi: org/10.1007/s11071-018-4663-6, 2018}). They proved both the local and global asymptotic stability of all equilibrium points except the interior one. This work extends their work and gives proof of both the local and global stability analysis of the interior equilibrium point. Numerical examples are also provided to substantiate the analytical findings.

math.DS↗