Browsing by Author "Soumitra Pal"

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A DELAY NONAUTONOMOUS PREDATOR-PREY MODEL for the EFFECTS of FEAR, REFUGE and HUNTING COOPERATION
(World Scientific, 2021) Pankaj Kumar Tiwari; Maitri Verma; Soumitra Pal; Yun Kang; Arvind Kumar Misra
Fear of predation may assert privilege to prey species by restricting their exposure to potential predators, meanwhile it can also impose costs by constraining the exploration of optimal resources. A predator-prey model with the effect of fear, refuge, and hunting cooperation has been investigated in this paper. The system's equilibria are obtained and their local stability behavior is discussed. The existence of Hopf-bifurcation is analytically shown by taking refuge as a bifurcation parameter. There are many ecological factors which are not instantaneous processes, and so, to make the system more realistic, we incorporate three discrete time delays: in the effect of fear, refuge and hunting cooperation, and analyze the delayed system for stability and bifurcation. Moreover, for environmental fluctuations, we further modify the delayed system by incorporating seasonality in the fear, refuge and cooperation. We have analyzed the seasonally forced delayed system for the existence of a positive periodic solution. In the support of analytical results, some numerical simulations are carried out. Sensitivity analysis is used to identify parameters having crucial impacts on the ecological balance of predator-prey interactions. We find that the rate of predation, fear, and hunting cooperation destabilizes the system, whereas prey refuge stabilizes the system. Time delay in the cooperation behavior generates irregular oscillations whereas delay in refuge stabilizes an otherwise unstable system. Seasonal variations in the level of fear and refuge generate higher periodic solutions and bursting patterns, respectively, which can be replaced by simple 1-periodic solution if the cooperation and fear are also allowed to vary with time in the former and latter situations. Higher periodicity and bursting patterns are also observed due to synergistic effects of delay and seasonality. Our results indicate that the combined effects of fear, refuge and hunting cooperation play a major role in maintaining a healthy ecological environment. © 2021 World Scientific Publishing Company.
CHAOTIC DYNAMICS of A STAGE-STRUCTURED PREY-PREDATOR SYSTEM with HUNTING COOPERATION and FEAR in PRESENCE of TWO DISCRETE DELAYS
(World Scientific, 2023) Soumitra Pal; Ashvini Gupta; Arvind Kumar Misra; Balram Dubey
Depending on behavioral differences, reproductive capability and dependency, the life span of a species is divided mainly into two classes, namely immature and mature. In this paper, we have studied the dynamics of a predator-prey system considering stage structure in prey and the effect of predator-induced fear with two discrete time delays: maturation delay and fear response delay. We consider that predators cooperate during hunting of mature prey and also include its impact in fear term. The conditions for existence of different equilibria, their stability analysis are carried out for non-delayed system and bifurcation results are presented extensively. It is observed that the fear parameter has stabilizing effect whereas the cooperative hunting factor having destabilizing effect on the system via occurrence of supercritical Hopf-bifurcation. Further, we observe that the system exhibits backward bifurcation between interior equilibrium and predator free equilibrium and hence the situation of bi-stability occurs in the system. Thereafter, we differentiate the region of stability and instability in bi-parametric space. We have also studied the system's dynamics with respect to maturation and fear response delay and observed that they also play a vital role in the system stability and occurrence of Hopf-bifurcation is shown with respect to both time delays. The system shows stability switching phenomenon and even higher values of fear response delay leads the system to enter in chaotic regime. The role of fear factor in switching phenomenon is discussed. Comprehensive numerical simulation and graphical presentation are carried out using MATLAB and MATCONT. © 2023 World Scientific Publishing Company.
Complex dynamics of a predator–prey system with fear and memory in the presence of two discrete delays
(Springer Science and Business Media Deutschland GmbH, 2023) Soumitra Pal; Ashvini Gupta; A.K. Misra; Balram Dubey
In this paper, we consider a two-species predator–prey model with fading memory, where the growth rate of prey species is subject to predation induced fear. Growth rate of predator species depends not only on the present density of prey but also on the past densities with diminishing impact. As the societal activities and behavioral practices influence carrying capacity of any species, we consider the density dependent carrying capacity of prey species instead of a constant. As fear on growth rate and societal activities on carrying capacity entail some time lags to show their effect, so we incorporate two delay parameters to corroborate this in the modeling phenomenon. Feasibility criteria of equilibria and their stability analysis are carried out. We observe that fear parameter and predation rate have destabilizing effect on the system’s dynamics, whereas parameter representing intensity of fading memory has stabilizing impact. We also distinguish stability and instability regions in different parametric planes. With increasing value of production factor from negative to positive, stability region decreases. The system also shows multiple stability switching phenomenon with respect to delay parameters. Solutions show chaotic behavior for a range of fear response delay both in the absence and presence of other delay parameter. © 2023, The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.
Dynamical behaviors of a constant prey refuge ratio-dependent prey-predator model with Allee and fear effects
(World Scientific, 2024) Soumitra Pal; Pijush Panday; Nikhil Pal; A.K. Misra; Joydev Chattopadhyay
In this paper, we consider a nonlinear ratio-dependent prey-predator model with constant prey refuge in the prey population. Both Allee and fear phenomena are incorporated explicitly in the growth rate of the prey population. The qualitative behaviors of the proposed model are investigated around the equilibrium points in detail. Hopf bifurcation including its direction and stability for the model is also studied. We observe that fear of predation risk can have both stabilizing and destabilizing effects and induces bubbling phenomenon in the system. It is also observed that for a fixed strength of fear, an increase in the Allee parameter makes the system unstable, whereas an increase in prey refuge drives the system toward stability. However, higher values of both the Allee and prey refuge parameters have negative impacts and the populations go to extinction. Further, we explore the variation of densities of the populations in different bi-parameter spaces, where the coexistence equilibrium point remains stable. Numerical simulations are carried out to explore the dynamical behaviors of the system with the help of MATLAB software. © 2024 World Scientific Publishing Company.
Fear effect in a three-species food chain model with generalist predator
(American Institute of Mathematical Sciences, 2024) Soumitra Pal; Pankaj Kumar Tiwari; Arvind Kumar Misra; Hao Wang
Within the framework of a food web, the foraging behavior of meso-carnivorous species is influenced by fear responses elicited by higher trophic level species, consequently diminishing the fecundity of these species. In this study, we investigate a three-species food chain model comprising of prey, an intermediate predator, and a top predator. We assume that both the birth rate and intraspecies competition of prey are impacted by fear induced by the intermediate predator. Additionally, the foraging behavior of the intermediate predator is constrained due to the presence of the top predator. It is essential to note that the top predators exhibit a generalist feeding behavior, encompassing food sources beyond the intermediate predators. The study systematically determines all feasible equilibria of the proposed model and conducts a comprehensive stability analysis of these equilibria. The investigation reveals that the system undergoes Hopf bifurcation concerning various model parameters. Notably, when other food sources significantly contribute to the growth of the top predators, the system exhibits stable behavior around the interior equilibrium. Our findings indicate that the dynamic influence of fear plays a robust role in stabilizing the system. Furthermore, a cascading effect within the system, stemming from the fear instigated by top predators, is observed and analyzed. Overall, this research sheds light on the intricate dynamics of fear-induced responses in shaping the stability and behavior of multi-species food web systems, highlighting the profound cascading effects triggered by fear mechanisms in the ecosystem. © 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
How can we avoid the extinction of any species naturally? A mathematical model
(World Scientific, 2024) A.K. Misra; Soumitra Pal; Yun Kang
A large number of herbivorous mammals and reptiles in many terrestrial ecosystems across the globe are presently in the receiving end of extinction. Over-exploitation by its immediate predator and anthropogenic actions is one of the main reasons. Reintroduction of apex predator or top predator at some instances has proven to be a successful strategy in restoring ecological balance. In this paper, we conceptualize the role of top predator in enriching the density of vulnerable species of lower trophic level, with the help of mathematical modeling. First, the dynamical behavior of two species system (prey and mesopredator) is studied, where growth of prey is subject to strong Allee effect. Also, the cost of predation induced fear is incorporated in the growth term. Parametric regions, for which the species perceive extinction risk are analyzed and depicted numerically. We consider that whenever density of the vulnerable species reach a certain threshold, minimum viable population, top predator is introduced in the habitat. Our obtained results show that a species population can be restored from the verge of extinction to a stable state with much higher population density with the introduction of top predator and even it stabilizes an oscillatory system. © 2024 World Scientific Publishing Company.
Impact of anthropogenic emissions of carbon dioxide and related temperature rise on wildlife population: A modeling study
(Elsevier B.V., 2024) Anjali Jha; Soumitra Pal; A.K. Misra
Climate change is driven by the increase in greenhouse gases in Earth's atmosphere, especially carbon dioxide (CO2), leading to a rise in the global average temperature. This temperature rise unleash far-reaching and profound consequences on various living organisms. In this research work, we formulate a nonlinear mathematical model to perceive the impact of rising temperature on wildlife species. In formulating the model, we take into account that the escalating CO2 concentration contributes to a rise in the global average temperature, thereby impacting the growth rate of wildlife population. We pinpoint the sufficient conditions for all the dynamic variables to reach their simultaneous equilibrium levels. The model analysis reveals a spectrum of bifurcations, including transcritical, Hopf, saddle–node, and Bogdanov–Takens bifurcations. Further, the examination of transcritical bifurcation led to the identification of a critical reduction rate of wildlife species due to human activities above which the wildlife population may teeter on the brink of extinction under the considered stressor of temperature rise. This extinction of wildlife species can be avoided by increasing the carrying capacity of forest biomass. Also, we have shown that for a specific set of parameter values, there exists a bistability between the forest-wildlife free equilibrium and the coexisting equilibrium. © 2024 International Association for Mathematics and Computers in Simulation (IMACS)
Impact of Fear and Group Defense on the Dynamics of a Predator-Prey System
(World Scientific, 2024) Soumitra Pal; Sarbari Karmakar; Saheb Pal; Nikhil Pal; A.K. Misra; Joydev Chattopadhyay
To reduce the chance of predation, many prey species adopt group defense mechanisms. While it is commonly believed that such defense mechanisms lead to positive feedback on prey density, a closer observation reveals that it may impact the growth rate of species. This is because individuals invest more time and effort in defense rather than reproductive activities. In this study, we delve into a predator-prey system where predator-induced fear influences the birth rate of prey, and the prey species exhibit group defense mechanism. We adopt a nonmonotonic functional response to govern the predator-prey interaction, which effectively captures the group defense mechanism. We present a detailed mathematical analysis, encompassing the determination of feasible equilibria and their stability conditions. Through the analytical approach, we demonstrate the occurrence of Hopf and Bogdanov-Takens (BT) bifurcations. We observe two distinct types of bistabilities in the system: one between interior and predator-free equilibria, and another between limit cycle and predator-free equilibrium. Our findings reveal that the parameters associated with group defense and predator-induced fear play significant roles in the survival and extinction of populations. © 2024 World Scientific Publishing Company.
Modeling the Effect of TV and Social Media Advertisements on the Dynamics of Vector-Borne Disease Malaria
(World Scientific, 2023) A.K. Misra; Soumitra Pal; Rabindra Kumar Gupta
Vector-borne disease malaria is transmitted to humans by arthropod vectors (mosquitoes) and contributes significantly to the global disease burden. TV and social media play a key role to disseminate awareness among people by broadcasting awareness programs. In this paper, a nonlinear model is formulated and analyzed in which cumulative number of advertisements through TV and social media is taken as dynamical variable that propagates awareness among people to control the prevalence of vector-borne disease. The human population is partitioned into susceptible, infected and aware classes, while the vector population is divided into susceptible and infected classes. Humans become infected and new cases arise when bitten by infected vectors (mosquitoes) and susceptible vectors get infected as they bite infected humans. The feasibility of equilibria is justified and their stability conditions are discussed. A crucial parameter, basic reproduction number, which measures the disease transmission potentiality is obtained. Bifurcation analysis is performed by varying the sensitive parameters, and it is found that the proposed system shows different kinds of bifurcations, such as transcritical bifurcation, saddle-node bifurcation and Hopf bifurcation, etc. The analysis of the model shows that reduction in vector population due to intervention of people of aware class would not efficiently reduce the infective cases, rather we have to minimize the transmission rates anyhow, to control the disease outbreak. © World Scientific Publishing Company.
Modeling the impact of precautionary measures and sanitation practices broadcasted through media on the dynamics of bacterial diseases
(Springer Science and Business Media Deutschland GmbH, 2023) Rabindra Kumar Gupta; Soumitra Pal; A.K. Misra
The media has a significant contribution in spreading awareness by broadcasting various programs about prevalent diseases in the society along with the role of providing information, feeding news and educating a large mass. In this paper, the effect of media programs promoting precautionary measures and sanitation practices to control the bacterial infection in the community is modeled and analyzed considering the number of media programs as a dynamical variable. In the modeling phenomena, human population is partitioned into three classes; susceptible, infected and recovered. The disease is supposed to spread by direct contact of susceptible with infected individuals and indirectly by the ingestion of bacteria present in the environment. The growth in the media programs is considered proportional to the size of infected population and the impact of these programs on the indirect disease transmission rate and bacteria shedding rate by infected individuals is also considered. The feasibility of equilibria and their stability conditions are obtained. Model analysis reveals that broadcasting media programs and increasing its effectiveness shrink the size of infected class and control the spread of disease to a large extent. © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.