Intraspecific competition of predator for prey with variable rates in protected areas
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ORIGINAL PAPER
Intraspecific competition of predator for prey with variable rates in protected areas Jai Prakash Tripathi · Debaldev Jana · N. S. N. V. K. Vyshnavi Devi · Vandana Tiwari · Syed Abbas
Received: 10 July 2020 / Accepted: 9 September 2020 © Springer Nature B.V. 2020
Abstract In this present study, we systematically explore the periodicity (almost periodic nature) of a dynamical system in time-varying environment, which portrays a special case of prey–predator model governed by non-autonomous differential equations. In particular, we investigate the dynamical characteristics of the underlying prey–predator model by considering modified Leslie–Gower-type model with Crowley– Martin functional response with time-dependent periodic variation of model parameters in a prey reserve area. We show the existence of globally stable periodic solutions. This perpetual prey oscillation results in persistent interference among predator, causing reduced feeding rate at high prey density. A comparative study J. P. Tripathi Department of Mathematics, Central University of Rajasthan, NH-8, Bandarsindri, Kishangarh, Ajmer, Rajasthan 305801, India D. Jana · N. S. N. V. K. Vyshnavi Devi Department of Mathematics and SRM Research Institute, SRM Institute of Science and Technology, Kattankulathur, Tamil Nadu 603203, India V. Tiwari Department of Applied Sciences and Humanities, K.N.I.T., Sultanpur, Uttar Pradesh 311001, India V. Tiwari Gandhi Smarak PG College, Samodhpur, Jaunpur, Uttar Pradesh 223102, India S. Abbas (B) School of Basic Sciences, Indian Institute of Technology Mandi, Mandi, HP 175005, India e-mail: [email protected]
between the two methods used to prove the existence of periodic (almost periodic) solution of the considered non-autonomous system is also discussed. After showing permanence, existence, uniqueness and global attractivity of the periodic (almost periodic) solution analytically, we demonstrate the typical prey and predator dynamics in time-varying environment using several numerical examples. Partial rank correlation coefficient technique is performed to address how the model output is affected by changes in a specific parameter disregarding the uncertainty over the rest of the parameters. Keywords Non-autonomous system · Temporal refuge · Almost periodic solution · Crowley–Martin functional response · Global attractivity · Continuation theorem, Sensitivity analysis Mathematics Subject Classification 37C60 · 34C27 · 47H11 · 49Q12
1 Introduction Process-based ecological models often include timedependent nonlinear processes [27,50], this suggests that the contribution of each parameter to the variation in model outputs may also change with time. For example, in forest growth models, the coupled nonlinear reduction in stomatal conductance and hydraulic conductivity as trees age will inevitably influence physio-
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logical processes such as photosynthesis, biomass allocation, etc. [27,43]. Thereby, some parameters influential at young stand ages may decline in influen
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