scholarly journals Three-Prey One-Predator Continuous Time Nonlinear System Model

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Jingyuan Zhang ◽  
Yan Yang
Keyword(s):  
Nonlinear System ◽  
Continuous Time ◽  
Order Differential Equation ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
System Model ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Simulation Results ◽  
Predator Model

In this paper, we propose a new multiple-prey one-predator continuous time nonlinear system model, in which the number of teams of preys is equal to 3; namely, a continuous time three-prey one-predator model is put forward and studied. The fourth-order differential equation is established, in which the prey teams help each other. The equilibrium points and stability are analyzed. When not considering preys help each other, we study the global stability and persistence of the model without help terms. The simulation results of system solutions with help terms corresponding to locally asymptotically stable equilibrium points and without help terms corresponding to globally asymptotically stable equilibrium points are given.

Efficient Continuous-Time Asymmetric Hopfield Networks for Memory Retrieval

2010 ◽  
Vol 22 (6) ◽  
pp. 1597-1614 ◽  
Author(s):  
Pengsheng Zheng ◽  
Wansheng Tang ◽  
Jianxiong Zhang
Keyword(s):  
Neural Networks ◽  
Continuous Time ◽  
Memory Retrieval ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Asymptotically Stable ◽  
Hopfield Networks ◽  
Energy Functions ◽  
Asymmetric Networks

A novel m energy functions method is adopted to analyze the retrieval property of continuous-time asymmetric Hopfield neural networks. Sufficient conditions for the local and global asymptotic stability of the network are proposed. Moreover, an efficient systematic procedure for designing asymmetric networks is proposed, and a given set of states can be assigned as locally asymptotically stable equilibrium points. Simulation examples show that the asymmetric network can act as an efficient associative memory, and it is almost free from spurious memory problem.

Chaos in the Periodically Parametrically Excited Lorenz System

2021 ◽  
Vol 31 (08) ◽  
pp. 2130024
Author(s):  
Weisheng Huang ◽  
Xiao-Song Yang
Keyword(s):  
Chaotic Dynamics ◽  
Lorenz System ◽  
Stable Equilibrium ◽  
Chaotic Behavior ◽  
Equilibrium Points ◽  
Time Varying ◽  
Asymptotically Stable ◽  
Parametrically Excited ◽  
The Lorenz System

We demonstrate in this paper a new chaotic behavior in the Lorenz system with periodically excited parameters. We focus on the parameters with which the Lorenz system has only two asymptotically stable equilibrium points, a saddle and no chaotic dynamics. A new mechanism of generating chaos in the periodically excited Lorenz system is demonstrated by showing that some trajectories can visit different attractor basins due to the periodic variations of the attractor basins of the time-varying stable equilibrium points when a parameter of the Lorenz system is varying periodically.

scholarly journals An Impulsively Controlled Three-Species Prey-Predator Model with Stage Structure and Birth Pulse for Predator

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Yanyan Hu ◽  
Mei Yan ◽  
Zhongyi Xiang
Keyword(s):  
Small Amplitude ◽  
Floquet Theory ◽  
Stage Structure ◽  
Critical Value ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Birth Pulse ◽  
Impulsive Equation ◽  
Predator Model ◽  
Predator System

We investigate the dynamic behaviors of a two-prey one-predator system with stage structure and birth pulse for predator. By using the Floquet theory of linear periodic impulsive equation and small amplitude perturbation method, we show that there exists a globally asymptotically stable two-prey eradication periodic solution when the impulsive period is less than some critical value. Further, we study the permanence of the investigated model. Our results provide valuable strategy for biological economics management. Numerical analysis is also inserted to illustrate the results.

scholarly journals Global Stability and Optimal Control of Dengue with Two Coexisting Virus Serotypes

MATEMATIKA ◽  
2019 ◽  
Vol 35 (4) ◽  
pp. 149-170
Author(s):  
Afeez Abidemi ◽  
Rohanin Ahmad ◽  
Nur Arina Bazilah Aziz
Keyword(s):  
Optimal Control ◽  
Global Stability ◽  
Disease Transmission ◽  
Deterministic Model ◽  
Control Strategies ◽  
Equilibrium Points ◽  
Effective Control ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Boundary Equilibrium

This study presents a two-strain deterministic model which incorporates Dengvaxia vaccine and insecticide (adulticide) control strategies to forecast the dynamics of transmission and control of dengue in Madeira Island if there is a new outbreak with a different virus serotypes after the first outbreak in 2012. We construct suitable Lyapunov functions to investigate the global stability of the disease-free and boundary equilibrium points. Qualitative analysis of the model which incorporates time-varying controls with the specific goal of minimizing dengue disease transmission and the costs related to the control implementation by employing the optimal control theory is carried out. Three strategies, namely the use of Dengvaxia vaccine only, application of adulticide only, and the combination of Dengvaxia vaccine and adulticide are considered for the controls implementation. The necessary conditions are derived for the optimal control of dengue. We examine the impacts of the control strategies on the dynamics of infected humans and mosquito population by simulating the optimality system. The disease-freeequilibrium is found to be globally asymptotically stable whenever the basic reproduction numbers associated with virus serotypes 1 and j (j 2 {2, 3, 4}), respectively, satisfy R01,R0j 1, and the boundary equilibrium is globally asymptotically stable when the related R0i (i = 1, j) is above one. It is shown that the strategy based on the combination of Dengvaxia vaccine and adulticide helps in an effective control of dengue spread in the Island.

scholarly journals Mathematical Modelling and Analysis of Corruption of Morals amongst Adolescents with Control Measures in Kenya

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Nathan Oigo Mokaya ◽  
Haileyesus Tessema Alemmeh ◽  
Cyrus Gitonga Ngari ◽  
Grace Gakii Muthuri
Keyword(s):  
Integrated Control ◽  
Equilibrium Points ◽  
Endemic Equilibrium ◽  
Control Measures ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Age Appropriate ◽  
Manifold Theory ◽  
Necessary And Sufficient ◽  
Well Posed

In the present paper, we formulate a new mathematical model for the dynamics of moral corruption with comprehensive age-appropriate sexual information and provision of guidance and counselling. The population is subdivided into three (3) different compartments according to their level of information on sexual matters. The model is proved to be both epidemiologically and mathematically well posed. The existence of unique morally corrupt-free and endemic equilibrium points is investigated. The basic reproduction number with respect to morally corrupt-free equilibrium is obtained using next generation matrix approach to monitor the dynamics of corrupt morals and ascertain its level in order to suggest effective intervention strategies to control this problem. The local as well as global asymptotic stability of these equilibrium points is studied. The analysis reveals a globally asymptotically stable morally corrupt-free equilibrium whenever ℛ 0 ≤ 1 and a globally asymptotically stable endemic equilibrium if otherwise. Further analysis, using center manifold theory, shows that the model exhibits forward bifurcation insinuating that the classical epidemiological requirement of ℛ 0 ≤ 1 is necessary and sufficient for elimination of moral corruption. A brief discussion on the graphical results using the available numerical procedures is shown. From numerical simulations, it was ascertain that integrated control strategy is the best approach to fight against moral corruption transmission. Lastly, some key parameters that show significance in the moral corruption elimination from the society are also exploited.

scholarly journals Global Stability of Malaria Transmission Dynamics Model with Logistic Growth

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Abadi Abay Gebremeskel
Keyword(s):  
Sensitivity Analysis ◽  
Global Stability ◽  
Malaria Transmission ◽  
Equilibrium Points ◽  
Transmission Dynamics ◽  
Logistic Growth ◽  
Asymptotically Stable ◽  
Dynamics Model ◽  
Globally Asymptotically Stable ◽  
The Impact

Mathematical models become an important and popular tools to understand the dynamics of the disease and give an insight to reduce the impact of malaria burden within the community. Thus, this paper aims to apply a mathematical model to study global stability of malaria transmission dynamics model with logistic growth. Analysis of the model applies scaling and sensitivity analysis and sensitivity analysis of the model applied to understand the important parameters in transmission and prevalence of malaria disease. We derive the equilibrium points of the model and investigated their stabilities. The results of our analysis have shown that if R0≤1, then the disease-free equilibrium is globally asymptotically stable, and the disease dies out; if R0>1, then the unique endemic equilibrium point is globally asymptotically stable and the disease persists within the population. Furthermore, numerical simulations in the application of the model showed the abrupt and periodic variations.

A New Approach for Estimating the Attraction Domain for Hopfield-Type Neural Networks

2009 ◽  
Vol 21 (1) ◽  
pp. 101-120 ◽  
Author(s):  
Dequan Jin ◽  
Jigen Peng
Keyword(s):  
Neural Networks ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Numerical Results ◽  
New Method ◽  
Attraction Domain ◽  
Network System ◽  
Asymptotically Stable ◽  
New Approach

In this letter, using methods proposed by E. Kaslik, St. Balint, and their colleagues, we develop a new method, expansion approach, for estimating the attraction domain of asymptotically stable equilibrium points of Hopfield-type neural networks. We prove theoretically and demonstrate numerically that the proposed approach is feasible and efficient. The numerical results that obtained in the application examples, including the network system considered by E. Kaslik, L. Brăescu, and St. Balint, indicate that the proposed approach is able to achieve better attraction domain estimation.

scholarly journals Addendum to ‘On an index policy for restless bandits'

1991 ◽  
Vol 23 (2) ◽  
pp. 429-430 ◽  
Author(s):  
Richard R. Weber ◽  
Gideon Weiss
Keyword(s):  
Equilibrium Point ◽  
Stable Equilibrium ◽  
Stable Equilibrium Point ◽  
Asymptotically Stable ◽  
Index Policy ◽  
Fluid Approximation ◽  
Globally Asymptotically Stable ◽  
Restless Bandits

We show that the fluid approximation to Whittle's index policy for restless bandits has a globally asymptotically stable equilibrium point when the bandits move on just three states. It follows that in this case the index policy is asymptotic optimal.

Sign in / Sign up

Export Citation Format

Share Document