scholarly journals Stability Analysis of Delayed Age-Structured Resource-Consumer Model of Population Dynamics With Saturated Intake Rate

2021 ◽  
Vol 9 ◽  
Author(s):  
Vitalii V. Akimenko
Keyword(s):  
Population Dynamics ◽  
Asymptotic Stability ◽  
Behavioral Change ◽  
Calorie Intake ◽  
Search Rate ◽  
Intake Rate ◽  
Local Asymptotic Stability ◽  
Consumer Population ◽  
Age Structured ◽  
Resource Patches

This article studies nonlinear n-resource-consumer autonomous system with age-structured consumer population. The model of consumer population dynamics is described by a delayed transport equation, and the dynamics of resource patches are described by ODE with saturated intake rate. The delay models the digestion period of generalist consumer and is included in the calorie intake rate, which impacts the consumer’s fertility and mortality. Saturated intake rate models the inhibition effect from the behavioral change of the resource patches when they react to the consumer population growing or from the crowding effect of the consumer. The conditions for the existence of trivial, semi-trivial, and non-trivial equilibria and their local asymptotic stability were obtained. The local asymptotic stability/instability of non-trivial equilibrium of a system with depleted patches is defined by new derived criteria, which relate the demographic characteristics of consumers with their search rate, growth rate of resource in patches, and behavioral change of the food resource when consumer population grows. The digestion period of a generalist consumer does not cause local asymptotical instabilities of consumer population at the semi-trivial and nontrivial equilibria. These theoretical results may be used in the study of metapopulation dynamics, desert locust populations dynamics, prey-predator interactions in fisheries, etc. The paper uses numerical experiments to confirm and illustrate all dynamical regimes of the n-resource-consumer population.

scholarly journals Stability Analysis of Delayed Age-structured Resource-Consumer Model of Population Dynamics with Saturated Intake Rate

2020 ◽  
Author(s):  
Vitalii V. Akimenko
Keyword(s):  
Population Dynamics ◽  
Behavioural Change ◽  
Calorie Intake ◽  
Intake Rate ◽  
Local Asymptotic Stability ◽  
Consumer Population ◽  
Age Structured ◽  
Resource Patches ◽  
Consumer Model ◽  
Theoretical Results

AbstractThe nonlinear n-resource-consumer autonomous system with age-structured consumer population is studied. While the model of consumer population dynamics is described by a delayed transport equation, the dynamics of resource patches are described by ordinary differential equations with saturated intake rate. The delay models the digestion period of generalist consumer and is included in the calorie intake rate which impacts on consumer’s fertility and mortality. Saturated intake rate models the inhibition effect from the behavioural change of the resource patches when they react on the consumer population growing or from the crowding effect of the consumer. The model is studied both analytically and numerically. Conditions for existence of trivial, semi-trivial and non-trivial equilibria and their local asymptotic stability are obtained. Numerical experiments confirm and illustrate these theoretical results.

Stability analysis of age-structured disabled population dynamics

2009 ◽  
Vol 43 (1) ◽  
pp. 72-74
Author(s):  
Peng Jigen ◽  
Song Xueli ◽  
Zhang Xiangqin
Keyword(s):  
Population Dynamics ◽  
Stability Analysis ◽  
Age Structured

Food supplementation and abundance estimation in the white-footed mouse

2006 ◽  
Vol 84 (8) ◽  
pp. 1210-1215 ◽  
Author(s):  
Pei-Jen L. Shaner
Keyword(s):  
Population Dynamics ◽  
Food Availability ◽  
Robust Design ◽  
Meta Analysis ◽  
Design Model ◽  
Food Supplementation ◽  
Abundance Estimates ◽  
Abundance Indices ◽  
Consumer Population ◽  
White Footed Mouse

Food availability often drives consumer population dynamics. However, food availability may also influence capture probability, which if not accounted for may create bias in estimating consumer abundance and confound the effects of food availability on consumer population dynamics. This study compared two commonly used abundance indices (minimum number alive (MNA) and number of animals captured per night per grid) with an abundance estimator based on robust design model as applied to the white-footed mouse ( Peromyscus leucopus (Rafinesque, 1818)) in food supplementation experiments. MNA consistently generated abundance estimates similar to the robust design model, regardless of food supplementation. The number of animals captured per night per grid, however, consistently generated lower abundance estimates compared with MNA and the robust design model. Nevertheless, the correlations between abundance estimates from MNA, number of animals captured, and robust design model were not influenced by food supplementation. This study demonstrated that food supplementation is not likely to create bias among these different measures of abundance. Therefore, there is a great potential for conducting meta-analysis of food supplementation effect on consumer population dynamics (particularly in small mammals) across studies using different abundance indices and estimators.

Local asymptotic stability for dissipative wave systems

1998 ◽  
Vol 104 (1) ◽  
pp. 29-50 ◽  
Author(s):  
Patrizia Pucci ◽  
James Serrin
Keyword(s):  
Asymptotic Stability ◽  
Local Asymptotic Stability

scholarly journals Global Stability and Hopf-bifurcation Analysis of Biological Systems using Delayed Extended Rosenzweig-MacArthur Model

2018 ◽  
Vol 12 (2) ◽  
pp. 171
Author(s):  
Enobong E. Joshua ◽  
Cec Ekemini T. Akpan
Keyword(s):  
Experimental Data ◽  
Population Dynamics ◽  
Hopf Bifurcation ◽  
Asymptotic Stability ◽  
Asymptotically Stable ◽  
Stability Switches ◽  
Large Delay ◽  
Local Hopf Bifurcation ◽  
Delay Margin ◽  
Theoretical Results

This paper investigates the global asymptotic stability of a Delayed Extended Rosenzweig-MacArthur Model via Lyapunov-Krasovskii functionals. Frequency sweeping technique ensures stability switches as the delay parameter increases and passes the critical bifurcating threshold.The model exhibits a local Hopf-bifurcation from asymptotically stable oscillatory behaviors to unstable strange chaotic behaviors dependent of the delay parameter values.Hyper-chaotic fluctuations were observed for large delay values far away from the critical delay margin. Numerical simulations of experimental data obtained via non-dimensionalization have shown the applications of theoretical results in ecological population dynamics.

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