Stability for a competing system of hierarchical age-structured populations

2020 ◽  
Vol 13 (07) ◽  
pp. 2050070
Author(s):  
Ze-Rong He ◽  
Nan Zhou
Keyword(s):  
Fixed Point ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Experiments ◽  
Structured Populations ◽  
Vital Rates ◽  
Partial Differential ◽  
Semigroup Method ◽  
Age Structured ◽  
The Stability

In this paper, we are concerned with the stability for a model in the form of system of integro-partial differential equations, which governs the evolution of two competing age-structured populations. The age-specified environment is incorporated in the vital rates, which displays the hierarchy of ages. By a non-zero fixed-point result, we show the existence of positive equilibria. Some conditions for the stability of steady states are derived by means of semigroup method. Furthermore, numerical experiments are also presented.

Numerical and Experimental Analysis of the Nonlinear Dynamics due to Impacts of a Continuous Overhung Rotor

1997 ◽  
Author(s):  
Mohammed F. Abdul Azeez ◽  
Alexander F. Vakakis
Keyword(s):  
Nonlinear Dynamics ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Experiments ◽  
The Other ◽  
Experimental Setup ◽  
Partial Differential ◽  
Qualitative Comparison ◽  
Set Up ◽  
Theory And Experiments

Abstract This work is aimed at obtaining the transient response of an overhung rotor when there are impacts occurring in the system. An overhung rotor clamped on one end, with a flywheel on the other and impacts occurring in between, due to a bearing with clearance, is considered. The system is modeled as a continuous rotor system and the governing partial differential equations are set up and solved. The method of assumed modes is used to discretize the system in order to solve the partial differential equations. Using this method numerical experiments are run and a few of the results are presented. The different numerical issues involved are also discussed. An experimental setup was built to run experiments and validate the results. Preliminary experimental observations are presented to show qualitative comparison of theory and experiments.

scholarly journals A spectral mapping theorem for semigroups solving PDEs with nonautonomous past

2003 ◽  
Vol 2003 (16) ◽  
pp. 933-951 ◽  
Author(s):  
Genni Fragnelli
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Spectral Mapping Theorem ◽  
Spectral Mapping ◽  
Partial Differential ◽  
The Stability

We prove a spectral mapping theorem for semigroups solving partial differential equations with nonautonomous past. This theorem is then used to give spectral conditions for the stability of the solutions of the equations.

scholarly journals Stability of observations of partial differential equations under uncertain perturbations

2017 ◽  
Vol 24 (1) ◽  
pp. 45-61 ◽  
Author(s):  
Martin Lazar
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Wave Operator ◽  
System Dynamic ◽  
Schrödinger Equations ◽  
Partial Differential ◽  
Main System ◽  
Different Types ◽  
The Stability ◽  
Observability Estimates

We demonstrate the stability of observability estimates for solutions to wave and Schrödinger equations subjected to additive perturbations. This work generalises recent averaged observability/control results by allowing for systems consisting of operators of different types. We also consider the simultaneous observability problem by which one tries to estimate the energy of each component of a system under consideration. Our analysis relies on microlocal defect tools, in particular on standard H-measures when the main system dynamic is governed by the wave operator, and parabolic H-measures in the case of the Schrödinger operator.

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