Differential Equations, Mathematical Biology, Population Dynamics, Ecological Modelling and Mathematical Bio Economics
34
Scopus Publications
Scopus Publications
THE IMPACT OF POLLUTION REDUCTION ON THE OPTIMAL HARVESTING STRATEGY IN A SEASONALLY CHANGING AND POLLUTED ENVIRONMENT Simon Zawka, P. D. N. Srinivasu Mathematics in Applied Sciences and Engineering, 2024 This paper deals with the optimal harvesting of single-species populations in a polluted and seasonally varying environment. The presence of pollution negatively impacts resource growth, and as a consequence, the economic rent from harvest suffers. Assuming that pollution is inevitable, the harvester, who has a fixed flow of funds for harvesting activity, intends to invest the unused funds left over after harvesting in pollution control, expecting some increment in the economic rent. Thus, optimal harvesting problems in two different scenarios have been studied, and the solutions are compared to evaluate the impact of investing in pollution reduction on revenues. Pontryagin's maximum principle and the concept of blocked intervals are used to solve the aforesaid problems. Findings of the study indicate that funding pollution control programs should be considered as an alternative to promote conservation of resources and enhance net economic rent for harvesting systems impacted by pollution and seasonal fluctuations.
OPTIMAL MANAGEMENT OF A PREY-PREDATOR SYSTEM IN A POLLUTED ENVIRONMENT WITH EFFORT SHARED BETWEEN POLLUTION REDUCTION AND HARVESTING Turkish World Mathematical Society Journal of Applied and Engineering Mathematics, 2024
Bio-economics of a renewable resource in the presence of pollution: The problem of optimal effort allocation Nonlinear Dynamics and Systems Theory, 2020
INFLUENCE of INVESTING in TREATING A POLLUTED ENVIRONMENT on the HARVEST: A PROBLEM of OPTIMAL ALLOCATION P. D. N. SRINIVASU, SIMON D. ZAWKA Journal of Biological Systems, 2019 This study is concerned with harvesting a renewable resource that is surviving in a polluted environment. Fall in the revenue from the resource due to presence of pollution in the environment drives the sole owner to allocate a part of the available effort towards treating the environment and the interest is to find the optimal allocation of the available effort towards harvesting the resource and treating the environment so that the revenue is maximized. Resource-pollution dynamics are studied, maximum sustainable yield and maximum sustainable revenue have been evaluated. Further, an optimal allocation problem has been formulated on infinite horizon and optimal solutions are obtained. Key results of the study are demonstrated through numerical illustrations.
Optimal harvesting for a single-species population governed by Gompertz law: Influence of environmental fluctuation and limited harvesting capacity P. D. N. Srinivasu, Simon D. Zawka International Journal of Biomathematics, 2019 This work presents an optimal harvesting problem associated with a single-species population governed by Gompertz law in a seasonally fluctuating environment. The influence of environmental fluctuation is accommodated by choosing the coefficients in the differential equation to be periodic functions with the same period and restriction on the harvesting effort is accommodated by considering binding constraints on the control variable. Hence, a linear optimal control problem has been considered where the state dynamics is governed by Gompertz equation and the control variable is subject to the binding constraints. With the help of maximum principle and the concept of blocked intervals, an optimal periodic solution has been obtained which is followed by the construction of optimal solution using the theory of most rapid approach. Important results of the study are demonstrated through numerical simulations.
Additional food supplements as a tool for biological conservation of predator-prey systems involving type III functional response: A qualitative and quantitative investigation P.D.N. Srinivasu, D.K.K. Vamsi, V.S. Ananth Journal of Theoretical Biology, 2018 Provision of additional food supplements for the purpose of biological conservation in ecosystems has of late been intensely researched by agriculturalists, biologists and mathematicians. The study of these ecosystems is usually done using the predator-prey systems. In these ecological studies it has been observed that the quality and quantity of additional food supplements provided play a crucial role in the growth of the predators and thereby influence the eventual state of the ecosystem. Also, in some of the ecological experiments it has been observed that predators exhibit non-optimal foraging behaviour in the presence of additional food. Findings also show that the predators exhibit a Holling type II response towards a target prey with predation highest at low prey densities. The results suggest that predation by predators is unlikely to stabilize low density prey populations. This can be attributed to the prey detectability independent nature of the type II response. In nature, sigmoidal functional responses such as the Holling type III response, have been documented in organisms from various taxa. In this kind of type III response the predators exhibit low detectability nature at low prey densities. Due to this the ecosystem tends to get stabilized at low prey densities avoiding the oscillations encountered in type II response. Motivated by these studies, in this paper, we consider a predator-prey system provided with additional food where the predator is assumed to exhibit Holling type III functional response towards the available food and the additional food supplements provided are assumed to be of constant density. We also assume that the predators are not optimal foragers. The model is analyzed in the control parameter space using the control parameters, quality and quantity of additional food. It is observed that the system exhibits apparent competition only when the predators are provided with high quality additional food supplements. Further, it has been shown that the ecosystem tends to get stabilized at low prey densities and the system can be steered to a desired state by a suitable choice of additional food supplements. Provision of low quality additional food supplements can result in completely opposite results to the expected ones.
Renewable resource management in a seasonally fluctuating environment with restricted harvesting effort Srinivasu D.N. Pichika, Simon D. Zawka Mathematical Biosciences, 2018 This paper presents bio-economics of a renewable resources in a seasonally changing environment in which the resource exploitation is subjected to restrictions on harvesting effort. The dynamics of the resource is assumed to be governed by the logistic equation. Seasonality is incorporated into the system by choosing the coefficients in the growth equation to be periodic functions with the same period. A linear optimal control problem involving binding constraints on the control variable has been considered. As a result the concept of blocked interval plays a key role in the construction of optimal solution. In view of the periodicity associated with the considered problem, we first construct an optimal periodic solution. The optimal solution is established using the most rapid approach path to the said optimal periodic solution. The global asymptotic stability property of the optimal periodic solution enables construction of a suboptimal solution. The optimal solution is found to be periodic after some finite time and suboptimal solution approaches the optimal periodic solution asymptotically. Key results are illustrated through numerical simulation.
Biological Conservation of Living Systems by Providing Additional Food Supplements in the Presence of Inhibitory Effect: A Theoretical Study Using Predator–Prey Models P. D. N. Srinivasu, D. K. K. Vamsi, I. Aditya Differential Equations and Dynamical Systems, 2018 Ecological and biological conservation of living systems has been an active area of research over the years by agriculturalists, biologists and mathematicians. One of the studies involves additional food supplement feeding (also called as diversionary feeding) for the purpose of biological (wildlife in some cases) conservation. The idea in this approach is to distract (thereby supplement) the wildlife from predating upon the other species with the end goal of wildlife conservation. On the other hand in agricultural entomology, insect control and optimization, additional food is supplemented as a tool for effective pest control thereby achieving the biological control. The study of these ecosystems is usually done using the predator–prey systems. In nature, we find situations wherein the group defense (toxicity) of the prey reduces the predator’s predation rate. This type of behaviour of the prey is also known as inhibitory effect of the prey. Biological conservation of such predator prey systems in the presence of additional food supplements is quite challenging and interesting. In this paper, we consider an additional food provided predator–prey system which is a variation of the standard predator–prey model in the presence of the inhibitory effect of the prey. The predators functional response is assumed to be of Holling type IV (considering the inhibitory effect). This model is analyzed to understand the inherent dynamics of the system. The findings suggest that the quality and quantity of additional food provided to the predators, play a very significant role in determining the eventual state of the ecosystem. The outcomes of the analysis suggests eco friendly strategies to eco-managers for biological conservation of living systems.
Integrated Approach for Modeling Coastal Lagoons: A Case for Chilka Lake, India S.R.V. Prasad Bhuvanagiri, Srinivasu Pichika, Raman Akkur, Kalavati Chaganti, Rakhesh Madhusoodhanan, et al. Handbook of Statistics, 2018 Coastal lagoons are transitional zones between land and sea: they are shallow inland water bodies, separated from the ocean by a barrier, but connected to it by one or more restricted inlets which remain open at least intermittently. Coastal lagoons are recognized world over for their ecological and economic value due to their contributions to agricultural, tourism industries, and fishery sectors. Ironically, however, they are also the most exploited water bodies through anthropogenic pressures which in turn affect the plants and animals inhabiting these areas. Sustainable management and restoration of such vulnerable ecosystems become the foremost challenges for the ecosystem managers. Chilka Lake, Asia's largest brackish water lagoon and a Ramsar site, is no exception. Chilka lagoon has been under considerable threat ecologically over the last two decades or so, and developing sustainable management strategies for the lagoon required a concerted study involving physical, chemical, and biological investigations at the ecosystem level or ecological modeling. In the present research held for period 5–6 years (2004–10), a Lagrangian approach was made to addressing some major issues concerning the lagoon such as factors that sustained the ecosystem so far and its further evolution. Such interdisciplinary approaches should help answer several ecological questions say, “when does large-scale hypoxia occur?” in such water bodies and what are the measures needed to avoid hypoxic events, etc. In the present study, we have made an attempt to understand the changes associated with biogeochemical cycles in the lagoon especially the dissolved oxygen and net ecosystem metabolism events. The study presented here unifies the physical/chemical/biological processes obtainable through monitoring the Chilka Lake via sound field observations with a modeling approach which is the essence of this study.
