Modeling the interaction of birds and small fish in a coastal lagoon
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Shashi Kant
Abstract
Coastal lagoons are high value productive and important systems for different projects. For example, aquaculture, fisheries and tourism are few of them. The quality of coastal waters in the ecosystems of lagoons can be greatly influenced by the growth of unwanted elements, e.g., excessive fisheries, tourism, etc. In this paper, a mathematical model is proposed and analysed to study the general and simplified form of an ecosystem of Chilika Lake, India. Chilika Lake (19°28′N–19°54′N and 85°06′E–85°36′E) is the largest wintering ground for migrating water fowl found anywhere on the Indian sub-continent. These migratory birds utilize the Chilika Lake for feeding, resting and breeding. The interaction of birds and small fish in the Chilika Lake is considered to be Leslie–Gower Holling type II. Since big fish are being sourced as income for local fishermen and the population of big fish is highly variable, and hence birds and small fishes are mainly the two types of biomass considered for this study. It must be noted that, in this study, we have considered the case of Chilika lake theoretically only and no practical data is collected for this study, and the name of Chilika is used only for better ecological understanding. Therefore, this theoretical study maybe linked to any such ecosystem. Their interaction is found mathematically, a two-dimensional continuous-time dynamical system modeling a simple predator–prey food chain. The dynamical system is represented in the form of two nonlinear coupled ordinary differential equation (ODE) systems. The main mathematical results are given in terms of boundedness of solutions, existence of equilibria, local and global stability of the coexisting interior point. An ecosystem in Indian coastal lagoons may suffer immediate environmental perturbations, such as depressions, tropical cyclones, earthquakes, epidemics, etc. To model such situations, the ODE model is further extended to a stochastic model driven by L
Acknowledgements
This study is theoretical, and no practical/primary data is collected from Chilika lake. It is also declared that related references have been suitably cited although if any reference left is just unintentional and assumed as cited. Also, it is declared that the views/ideas expressed in this article belong to the author, and the organization to which the author belongs need not necessarily agree with these views/ideas.
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Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: None declared.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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© 2021 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Original Research Articles
- Robust optimization of multistage process: response surface and multi-response optimization approaches
- Effects of uniform or non-uniform heating at bottom wall on MHD mixed convection in a porous cavity saturated by nanofluid
- Unsteady MHD free convection flow past a vertical permeable flat plate in a rotating frame of reference with constant heat source and variable thermal boundary condition in a nanofluid
- Modeling the interaction of birds and small fish in a coastal lagoon
- Microcontroller-based simulation of a nonlinear resistive-capacitive-inductance shunted Josephson junction model and applications in electromechanical engineering
- Adaptive level set method applied to drag minimization problems constrained by Stokes equations
- Solving calculus of variation problems via multiquadric radial basis function method with optimal shape parameter
- Effect of moving stretching sheets on natural convection in partially heated square cavity filled with nanofluid
- On the dynamics and control of a new fractional difference chaotic map
- Retraction
- Retraction of: algebro-geometric constructions of the Heisenberg hierarchy
Articles in the same Issue
- Frontmatter
- Original Research Articles
- Robust optimization of multistage process: response surface and multi-response optimization approaches
- Effects of uniform or non-uniform heating at bottom wall on MHD mixed convection in a porous cavity saturated by nanofluid
- Unsteady MHD free convection flow past a vertical permeable flat plate in a rotating frame of reference with constant heat source and variable thermal boundary condition in a nanofluid
- Modeling the interaction of birds and small fish in a coastal lagoon
- Microcontroller-based simulation of a nonlinear resistive-capacitive-inductance shunted Josephson junction model and applications in electromechanical engineering
- Adaptive level set method applied to drag minimization problems constrained by Stokes equations
- Solving calculus of variation problems via multiquadric radial basis function method with optimal shape parameter
- Effect of moving stretching sheets on natural convection in partially heated square cavity filled with nanofluid
- On the dynamics and control of a new fractional difference chaotic map
- Retraction
- Retraction of: algebro-geometric constructions of the Heisenberg hierarchy
