scholarly journals Qualitative Analysis of a Retarded Mathematical Framework with Applications to Living Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Carlo Bianca ◽  
Massimiliano Ferrara ◽  
Luca Guerrini
Keyword(s):  
Qualitative Analysis ◽  
Carrying Capacity ◽  
Time Lag ◽  
Sufficient Conditions ◽  
Logistic Equation ◽  
Living Systems ◽  
Hopf Bifurcations ◽  
Economic Systems ◽  
Mathematical Framework ◽  
The Stability

This paper deals with the derivation and the mathematical analysis of an autonomous and nonlinear ordinary differential-based framework. Specifically, the mathematical framework consists of a system of two ordinary differential equations: a logistic equation with a time lag and an equation for the carrying capacity that is assumed here to be time dependent. The qualitative analysis refers to the stability analysis of the coexistence equilibrium and to the derivation of sufficient conditions for the existence of Hopf bifurcations. The results are of great interest in living systems, including biological and economic systems.

Persistence, Turing Instability and Hopf Bifurcation in a Diffusive Plankton System with Delay and Quadratic Closure

2016 ◽  
Vol 26 (03) ◽  
pp. 1650047 ◽  
Author(s):  
Jiantao Zhao ◽  
Junjie Wei
Keyword(s):  
Hopf Bifurcation ◽  
Center Manifold ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Turing Instability ◽  
Positive Equilibrium ◽  
Hopf Bifurcations ◽  
System With Delay ◽  
The Stability ◽  
Theoretical Results

A reaction–diffusion plankton system with delay and quadratic closure term is investigated to study the interactions between phytoplankton and zooplankton. Sufficient conditions independent of diffusion and delay are obtained for the persistence of the system. Our conclusions show that diffusion can induce Turing instability, delay can influence the stability of the positive equilibrium and induce Hopf bifurcations to occur. The computational formulas which determine the properties of bifurcating periodic solutions are given by calculating the normal form on the center manifold, and some numerical simulations are carried out for illustrating the theoretical results.

Stability and Bifurcation Analysis in a Delayed Predator-Prey Model with Stage-Structure and Harvesting

2010 ◽  
Vol 143-144 ◽  
pp. 1358-1363
Author(s):  
Zhi Chao Jiang ◽  
Ming Wei Nie
Keyword(s):  
Bifurcation Analysis ◽  
Sufficient Conditions ◽  
Stage Structure ◽  
Hopf Bifurcations ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Stability And Bifurcation Analysis ◽  
Characteristic Values ◽  
The Stability

In this paper, we investigate a delayed stage-structured predator-prey model with continuous harvesting on prey. Positivity and boundness of solutions and sufficient conditions of the stability of equilibria are obtained. Using and as bifurcation parameters, the existence of Hopf bifurcations at equilibria is established by analyzing the distribution of the characteristic values.

scholarly journals Stability and Bifurcation Analysis on a Predator–Prey System with the Weak Allee Effect

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 432 ◽  
Author(s):  
Jianming Zhang ◽  
Lijun Zhang ◽  
Yuzhen Bai
Keyword(s):  
Allee Effect ◽  
Center Manifold ◽  
Sufficient Conditions ◽  
Hopf Bifurcations ◽  
Stability Switches ◽  
Predator Prey ◽  
Prey System ◽  
Stability And Bifurcation Analysis ◽  
The Stability ◽  
Bifurcation And Stability

In this paper, the dynamics of a predator-prey system with the weak Allee effect is considered. The sufficient conditions for the existence of Hopf bifurcation and stability switches induced by delay are investigated. By using the theory of normal form and center manifold, an explicit expression, which can be applied to determine the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions, are obtained. Numerical simulations are performed to illustrate the theoretical analysis results.

Analysis of a Delayed Predator–Prey System with Harvesting

2018 ◽  
Vol 19 (3-4) ◽  
pp. 335-349
Author(s):  
Wei Liu ◽  
Yaolin Jiang
Keyword(s):  
Center Manifold ◽  
Differential Algebra ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Positive Equilibrium ◽  
Hopf Bifurcations ◽  
Center Manifold Reduction ◽  
Predator Prey ◽  
Prey System ◽  
The Stability

AbstractThis article is concerned with a Leslie–Gower predator–prey system with the predator being harvested and the prey having a delay due to the gestation of prey species. By regarding the gestation delay as a bifurcation parameter, we first derive some sufficient conditions on the stability of positive equilibrium point and the existence of Hopf bifurcations basing on the local parametrization method for differential-algebra system. In succession, we also investigate the direction of Hopf bifurcations and the stability of bifurcating periodic solutions on the center manifold by employing the center manifold reduction for functional differential equations. Finally, to verify our theoretical predictions, several numerical simulations are given.

Qualitative Analysis of a Competitive Lotka-Volterra System with Stage Structure in Mechanics Engineering

2013 ◽  
Vol 312 ◽  
pp. 60-65
Author(s):  
Huan Tao Zhu ◽  
Hong Shi Wang
Keyword(s):  
Qualitative Analysis ◽  
Sufficient Conditions ◽  
Stage Structure ◽  
Positive Equilibrium ◽  
Volterra System ◽  
Structured Model ◽  
The Stability

In this paper, a stage structured model with delay that competition occurs between the two adults of species is studied. The permanence and the stability of the nonnegative equilibrium are analyzed. Some sufficient conditions which guarantee the permanence of the system and the stability of the boundary and positive equilibrium are obtained respectively.

scholarly journals Analysis of a Viral Infection Model with Delayed Nonlytic Immune Response

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Mengye Chen ◽  
Liang You ◽  
Jie Tang ◽  
Shasha Su ◽  
Ruiming Zhang
Keyword(s):  
Immune Response ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Infection Model ◽  
Hopf Bifurcations ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
The Stability ◽  
Virus Infection Model ◽  
Viral Infection Model

We investigate the dynamical behavior of a virus infection model with delayed nonlytic immune response. By analyzing corresponding characteristic equations, the local stabilities of two boundary equilibria are established. By using suitable Lyapunov functional and LaSalle’s invariance principle, we establish the global stability of the infection-free equilibrium. We find that the infection free equilibriumE0is globally asymptotically stable whenR0⩽1, and the infected equilibrium without immunityE1is local asymptotically stable when1<R0⩽1+bβ/cd. Under the conditionR0>1+bβ/cdwe obtain the sufficient conditions to the local stability of the infected equilibrium with immunityE2. We show that the time delay can change the stability ofE2and lead to the existence of Hopf bifurcations. The stabilities of bifurcating periodic solutions are studied and numerical simulations to our theorems are provided.

scholarly journals Qualitative Analysis of a Leslie-Gower Predator-Prey System with Nonlinear Harvesting in Predator

2016 ◽  
Vol 2016 ◽  
pp. 1-15 ◽  
Author(s):  
Manoj Kumar Singh ◽  
B. S. Bhadauria ◽  
Brajesh Kumar Singh
Keyword(s):  
Complex Dynamics ◽  
Sufficient Conditions ◽  
Hopf Bifurcations ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Proposed Model ◽  
Nonlinear Harvesting ◽  
The Stability ◽  
Constant Yield

This paper deals with the study of the stability and the bifurcation analysis of a Leslie-Gower predator-prey model with Michaelis-Menten type predator harvesting. It is shown that the proposed model exhibits the bistability for certain parametric conditions. Dulac’s criterion has been adopted to obtain the sufficient conditions for the global stability of the model. Moreover, the model exhibits different kinds of bifurcations (e.g., the saddle-node bifurcation, the subcritical and supercritical Hopf bifurcations, Bogdanov-Takens bifurcation, and the homoclinic bifurcation) whenever the values of parameters of the model vary. The analytical findings and numerical simulations reveal far richer and complex dynamics in comparison to the models with no harvesting and with constant-yield predator harvesting.

scholarly journals Engineering motile aqueous phase-separated droplets via liposome stabilisation

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Shaobin Zhang ◽  
Claudia Contini ◽  
James W. Hindley ◽  
Guido Bolognesi ◽  
Yuval Elani ◽  
...  
Keyword(s):  
Aqueous Phase ◽  
Marangoni Effect ◽  
Living Systems ◽  
Biological Processes ◽  
Biological Applications ◽  
Emulsion System ◽  
Biotechnological Potential ◽  
New Directions ◽  
Directional Motion ◽  
The Stability

AbstractThere are increasing efforts to engineer functional compartments that mimic cellular behaviours from the bottom-up. One behaviour that is receiving particular attention is motility, due to its biotechnological potential and ubiquity in living systems. Many existing platforms make use of the Marangoni effect to achieve motion in water/oil (w/o) droplet systems. However, most of these systems are unsuitable for biological applications due to biocompatibility issues caused by the presence of oil phases. Here we report a biocompatible all aqueous (w/w) PEG/dextran Pickering-like emulsion system consisting of liposome-stabilised cell-sized droplets, where the stability can be easily tuned by adjusting liposome composition and concentration. We demonstrate that the compartments are capable of negative chemotaxis: these droplets can respond to a PEG/dextran polymer gradient through directional motion down to the gradient. The biocompatibility, motility and partitioning abilities of this droplet system offers new directions to pursue research in motion-related biological processes.

On the Necessary and Sufficient Conditions for the Stability of Linear Generalized Ordinary Differential, Linear Impulsive and Linear Difference Systems

2009 ◽  
Vol 16 (4) ◽  
pp. 597-616
Author(s):  
Shota Akhalaia ◽  
Malkhaz Ashordia ◽  
Nestan Kekelia
Keyword(s):  
Linear System ◽  
Difference Equations ◽  
Closed Interval ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Difference Systems ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Generalized Ordinary Differential Equations ◽  
Lyapunov Sense

Abstract Necessary and sufficient conditions are established for the stability in the Lyapunov sense of solutions of a linear system of generalized ordinary differential equations 𝑑𝑥(𝑡) = 𝑑𝐴(𝑡) · 𝑥(𝑡) + 𝑑𝑓(𝑡), where and are, respectively, matrix- and vector-functions with bounded total variation components on every closed interval from . The results are realized for the linear systems of impulsive, ordinary differential and difference equations.

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