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Your search keyword '"Upadhyay, Ranjit Kumar"' showing total 2 results
Start Over Author "Upadhyay, Ranjit Kumar" Topic chaos Topic mathematical models Publication Year Range Last 50 years
2 results on '"Upadhyay, Ranjit Kumar"'

1. On the explosive instability in a three-species food chain model with modified Holling type IV functional response.

Author

Parshad, Rana D., Upadhyay, Ranjit Kumar, Mishra, Swati, Tiwari, Satish Kumar, and Sharma, Swarnali

Subjects
*MATHEMATICAL models, *DIFFERENTIAL equations, *HOPF bifurcations, *MATHEMATICAL analysis, *PARAMETERS (Statistics)
Abstract

In earlier literature, a version of a classical three-species food chain model, with modified Holling type IV functional response, is proposed. Results on the global boundedness of solutions to the model system under certain parametric restrictions are derived, and chaotic dynamics is shown. We prove that in fact the model possesses explosive instability, and solutions can explode/blow up in finite time, for certain initial conditions, even under the parametric restrictions of the literature. Furthermore, we derive the Hopf bifurcation criterion, route to chaos, and Turing bifurcation in case of the spatially explicit model. Lastly, we propose, analyze, and simulate a version of the model, incorporating gestation effect, via an appropriate time delay. The delayed model is shown to possess globally bounded solutions, for any initial condition. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Published
2017
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2. Modeling spatiotemporal dynamics of vole populations in Europe and America

Author

Upadhyay, Ranjit Kumar, Kumari, Nitu, and Rai, Vikas

Subjects
*MATHEMATICAL models, *VOLES, *DIFFUSION, *ECOLOGY of predatory animals, *DATA analysis
Abstract

Abstract: The mathematical models proposed and studied in the present paper provide a unified framework to understand complex dynamical patterns in vole populations in Europe and North America. We have extended the well-known model provided by Hanski and Turchin by incorporating the diffusion term and spatial heterogeneity and performed several mathematical and numerical analyses to explore the dynamics in space and time of the model. These models successfully predicted the observed rodent dynamics in these regions. An attempt has been made to bridge the gap between the field and theoretical studies carried out by Turchin and Hanski (1997) and Turchin and Ellner (2000) . Simulation experiments, mainly two-dimensional parameter scans, show the importance of spatial heterogeneity in order to understand the poorly understood fluctuations in population densities of voles in Fennoscandia and Northern America. This study shed new light upon the dynamics of voles in these regions. The nonlinear analysis of vole data suggests that the dynamical shift is from stability to chaos. Diffusion driven model systems predict a new type of dynamics not yet observed in the field studies of vole populations carried out so far. This has been termed as chaotic in time and regular in space (CTRS). We observed CTRS dynamics in several simulation experiments. This directs us to expect that dynamics of this animal would be de-correlated in time and simultaneously mass extinctions might be possible at many spatial locations. [Copyright &y& Elsevier]

Published
2010
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