arXiv subjects

Malay Banerjee

Publications and source records attributed to Malay Banerjee.

26 records · Page 2Linked to original sources

arXiv2021

Effect of light intensity on resonance patterns in CDIMA reaction

Photosensitive CDIMA reaction-diffusion equation is considered to explain the resonance in the linearly coupled system. The conditions for Turing instability is obtained for the coupled reaction-diffusion system. Also, determining the critical diffusion coefficients for exiting the resonance type pattern is also discussed with analytical conditions. The photosensitive effect on $3:1$ resonance forcing is studied in the presence of strong and weak couplings. Numerical simulations are performed to validate the theoretical findings.

nlin.PS↗

arXiv2021

Stationary and non-stationary pattern formation over fragmented habitat

Spatio-temporal pattern formation over the square and rectangular domain has received significant attention from researchers. A wide range of stationary and non-stationary patterns produced by two interacting populations is abundant in the literature. Fragmented habitats are widespread in reality due to the irregularity of the landscape. This work considers a prey-predator model capable of producing a wide range of stationary and time-varying patterns over a complex habitat. The complex habitat is assumed to have consisted of two rectangular patches connected through a corridor. Our main aim is to explain how the shape and size of the fragmented habitat regulate the spatio-temporal pattern formation at the initial time. The analytical conditions are derived to ensure the existence of a stationary pattern and illustrate the role of most unstable eigenmodes to determine the number of patches for the stationary pattern. Exhaustive numerical simulations help to explain the spatial domain's size and shape on the transient patterns and the duration of transient states.

math.DS↗

arXiv2021

Oscillations and pattern formation in a slow-fast prey-predator system

We consider the properties of a slow-fast prey-predator system in time and space. We first argue that the simplicity of prey-predator system is apparent rather than real and there are still many of its hidden properties that have been poorly studied or overlooked altogether. We further focus on the case where, in the slow-fast system, the prey growth is affected by a weak Allee effect. We first consider this system in the non-spatial case and make its comprehensive study using a variety of mathematical techniques. In particular, we show that the interplay between the Allee effect and the existence of multiple timescales may lead to a regime shift where small-amplitude oscillations in the population abundances abruptly change to large-amplitude oscillations. We then consider the spatially explicit slow-fast prey-predator system and reveal the effect of different time scales on the pattern formation. We show that a decrease in the timescale ratio may lead to another regime shift where the spatiotemporal pattern becomes spatially correlated leading to large-amplitude oscillations in spatially average population densities and potential species extinction.

math.DS↗

arXiv2020

Immuno-epidemiological model of two-stage epidemic growth

Epidemiological data on seasonal influenza show that the growth rate of the number of infected individuals can increase passing from one exponential growth rate to another one with a larger exponent. Such behavior is not described by conventional epidemiological models. In this work an immuno-epidemiological model is proposed in order to describe this two-stage growth. It takes into account that the growth in the number of infected individuals increases the initial viral load and provides a passage from the first stage of epidemic where only people with weak immune response are infected to the second stage where people with strong immune response are also infected. This scenario may be viewed as an increase of the effective number of susceptible increasing the effective growth rate of infected.

q-bio.PE↗

arXiv2020

On a quarantine model of coronavirus infection and data analysis

Attempts to curb the spread of coronavirus by introducing strict quarantine measures apparently have different effect in different countries: while the number of new cases has reportedly decreased in China and South Korea, it still exhibit significant growth in Italy and other countries across Europe. In this brief note, we endeavour to assess the efficiency of quarantine measures by means of mathematical modelling. Instead of the classical SIR model, we introduce a new model of infection progression under the assumption that all infected individual are isolated after the incubation period in such a way that they cannot infect other people. Disease progression in this model is determined by the basic reproduction number $\mathcal{R}_0$ (the number of newly infected individuals during the incubation period), which is different compared to that for the standard SIR model. If $\mathcal{R}_0 >1$, then the number of latently infected individuals exponentially grows. However, if $\mathcal{R}_0 <1$ (e.g.~due to quarantine measures and contact restrictions imposed by public authorities), then the number of infected decays exponentially. We then consider the available data on the disease development in different countries to show that there are three possible patterns: growth dynamics, growth-decays dynamics, and patchy dynamics (growth-decay-growth). Analysis of the data in China and Korea shows that the peak of infection (maximum of daily cases) is reached about 10 days after the restricting measures are introduced. During this period of time, the growth rate of the total number of infected was gradually decreasing. However, the growth rate remains exponential in Italy. Arguably, it suggests that the introduced quarantine is not sufficient and stricter measures are needed.

q-bio.PE↗

arXiv2016

Modelling of cell choice between differentiation and apoptosis on the basis of intracellular and extracellular regulations and stochasticity

The work is devoted to the analysis of cell population dynamics where cells make a choice between differentiation and apoptosis. This choice is based on the values of intracellular proteins whose concentrations are described by a system of ordinary differential equations with bistable dynamics. Intracellular regulation and cell fate are controlled by the extracellular regulation through the number of differentiated cells. Initial intracellular protein concentrations are considered for each cell as random variables with a given area of variation. Intracellular regulation, extracellular regulation and random initial conditions work together to produce differentiated cells and to control their number. The role of intracellular regulation is to provide a possible choice between differentiation and apoptosis, extracellular regulation controls the number of differentiated cells, stochastic initial conditions can suppress oscillations and provide stability of the system.

q-bio.CB↗

arXiv2015

Spatiotemporal pattern formation in a prey-predator model under environmental driving forces

Many existing studies on pattern formation in the reaction-diffusion systems rely on deterministic models. However, environmental noise is often a major factor which leads to significant changes in the spatiotemporal dynamics. In this paper, we focus on the spatiotemporal patterns produced by the predator-prey model with ratio-dependent functional response and density dependent death rate of predator. We get the reaction-diffusion equations incorporating the self-diffusion terms, corresponding to random movement of the individuals within two dimensional habitats, into the growth equations for the prey and predator population. In order to have to have the noise added model, small amplitude heterogeneous perturbations to the linear intrinsic growth rates are introduced using uncorrelated Gaussian white noise terms. For the noise added system, we then observe spatial patterns for the parameter values lying outside the Turing instability region. With thorough numerical simulations we characterize the patterns corresponding to Turing and Turing-Hopf domain and study their dependence on different system parameters like noise-intensity, etc.

q-bio.PE↗

arXiv2014

Maximizing a psychological uplift in love dynamics

In this paper, we investigate the dynamical properties of a psychological uplift in lovers. We first evaluate extensively the dynamical equations which were recently given by Rinaldi et. al., Physica A 392, pp.3231-3239 (2013). Then, the dependences of the equations on several parameters are numerically examined. From the view point of lasting partnership for lovers, especially, for married couples, one should optimize the parameters appearing in the dynamical equations to maintain the love for their respective partners. To achieve this optimization, we propose a new idea where the parameters are stochastic variables and the parameters in the next time step are given as expectations over a Boltzmann-Gibbs distribution at a finite temperature. This idea is very general and might be applicable to other models dealing with human relationships.

physics.soc-ph↗