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Apr 30, 2021Open    AccessArticle

Dynamically Consistent NSFD Discretization of Some Productive-Destructive Population Models Satisfying Conservations Laws

Dominic P. Clemence-Mkhope
In this article, two general construction methods of nonstandard finite difference (NSFD) models are considered for productive-destructive models that also satisfy conservation laws: one for productive-destructive (PD) and the other for conservative systems. It is observed that the general NSFD method for PD systems may not result in numerical models for such systems that are dynamically consistent with respect to the conservation laws. This is illustrated through two examples, with one satisfyi...
Open Access Library J. Vol.8, 2021
Doi:10.4236/oalib.1107077


Mar 26, 2021Open    AccessArticle

Stability, Chaos Diagnose and Adaptive Control of Two Dimensional Discrete - Time Dynamical System

Maysoon M. Aziz, Omar M. Jihad
In this paper 2D discrete time dynamical system is presented. The fixed points were found. The stability of fixed points is measured by characteristic roots, jury criteria, Lyapunov function. All show that the system is unstable, and analyzing the dynamic behavior of the system finds bifurcation diagrams at the bifurcation parameter. Newton’s Raphson numerical method was used the roots of the system with the minimum error. Then, chaoticity is measured by the phase space; maximum Lyapunov exponen...
Open Access Library J. Vol.8, 2021
Doi:10.4236/oalib.1107270


Oct 15, 2020Open    AccessArticle

A Fractional Order Model for the Transmission Dynamics of Measles with Vaccination

Nnaemeka S. Aguegboh, Nkem R. Nwokoye, Netochukwu E. Onyiaji, Ogechi R. Amanso, Dominic O. Oranugo
In this paper, the fractional order model was adopted to describe the dynamics of measles and to establish how the virus that causes measles is transmitted as well as how to mitigate the conditions that cause the spread. We showed the existence of the equilibrium states. The threshold parameter of the model was evaluated in terms of parameters in the model using the next generation matrix approach. We provided the conditions for the stability of the disease free and the endemic equilibrium point...
Open Access Library J. Vol.7, 2020
Doi:10.4236/oalib.1106670


Jul 29, 2020Open    AccessArticle

A Three-Dimensional Chaotic System and Its New Proposed Electronic Circuit

Maysoon M. Aziz, Dalya M. Merie
In this paper, new electronic circuit was designed with two-equilibrium as an engineering application on a three-dimensional chaotic system. The circuit consists of resistors, capacitors, voltages and operational amplifiers TL032CN. The adopted continuous-time chaotic dynamical system is with quadratic cross-product nonlinear terms and parameters. The basic characteristics of the proposed circuit model were analyzed in detail by equilibrium points, stability analysis, Lyapunov exponents and Kapl...
Open Access Library J. Vol.7, 2020
Doi:10.4236/oalib.1106555


Apr 20, 2020Open    AccessArticle

Homoclinic Points and Homoclinic Orbits for the Quadratic Family of Real Functions with Two Parameters

Karam N. Abdul-Kareem, Salma M. Farris
In this work, we study the homoclinic points and homoclinic orbits of the family of real functions with two parameters. We show that the function has no homoclinic points for , but has a homoclinic point for . Also, we prove that has homoclinic orbits for .
Open Access Library J. Vol.7, 2020
Doi:10.4236/oalib.1106170


Feb 28, 2020Open    AccessArticle

Stability and Adaptive Control with Sychronization of 3-D Dynamical System

Maysoon M. Aziz, Dalya M. Merie
A three-dimensional system is presented with unknown parameters that employs two nonlinearities terms. The basic characteristics of the system are studied. The stability is measured by Characteristic equation roots, Routh stability criteria, Hurwitz stability criteria and Lapiynov function, all show that the system unstable. Then, Chaoticity is measured by maximum Lapiynov exponent of (Lmax=2.509426) and “Kaplan-Yorke” dimension (DL
...
Open Access Library J. Vol.7, 2020
Doi:10.4236/oalib.1106075


Jul 04, 2019Open    AccessArticle

A Note on Momentum Conservation in the Non-Relativistic Lorentz Theory of Radiation Reaction

Rajat Roy
The Lorentz theory of radiation reaction in the non relativistic limit is critically examined from the principles of symmetry. In Newtonian motion the applied force and the consequent momentum change generally always have a direction. In the case of a charged body this momentum change is accompanied by the radiation of photons. The question that needs to be answered is: does this radiated field carry any mo
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Open Access Library J. Vol.6, 2019
Doi:10.4236/oalib.1105534


Jun 26, 2018Open    AccessArticle

Chaos, Mixing, Weakly Mixing and Exactness

Mohammed Nokhas Murad Kaki
In this paper, new definitions of chaos, exact chaos, mixing chaos, and weak mixing chaos called θ-chaos, θ exact chaos, θ-mixing chaos are introduced and extended to topological spaces. Our purpose is to investigate other t
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Open Access Library J. Vol.5, 2018
Doi:10.4236/oalib.1103773


Feb 23, 2018Open    AccessArticle

Spreading Dynamic of a PLSGP Giving up Smoking Model on Scale-Free Network

Yanling Fei, Xiongding Liu
A new PLSGP (potential smokers-light smokers-persistent smokers-giving up smokers-potential smokers) model with birth and death rates on complex heterogeneous networks is presented. Using the mean-field theory, we obtain the basic reproduction number R0 and find that basic reproduction number for constant contact is independent of the topology of the underlying networks. When R0<1, the smoki
...
Open Access Library J. Vol.5, 2018
Doi:10.4236/oalib.1104365


Nov 09, 2016Open    AccessArticle

Backstepping Technique Based on Error

Li Wang
Backstepping technique usually adopts back step design to construct the Lyapunov function gradually, and then to design the corresponding virtue controller. The backstepping technique based on error also adopts back step design process, but the design of virtue controllers depends on the corresponding errors which are designed to satisfy some expected behaviors. Six different error equations are deduced by chang
...
Open Access Library J. Vol.3, 2016
Doi:10.4236/oalib.1103061


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