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Ordinary Differential Equations and Applied Dynamics

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Full-Text Articles in Dynamic Systems

Quartic Autocatalytic Chemical Reaction Of A Non-Newtonian Based Ternary Hybrid Nanofluid, Tunde M. Ajayi, Amos Wale Ogunsola, Olusegun Adebayo Ajala Oct 2023

Quartic Autocatalytic Chemical Reaction Of A Non-Newtonian Based Ternary Hybrid Nanofluid, Tunde M. Ajayi, Amos Wale Ogunsola, Olusegun Adebayo Ajala

International Journal of Emerging Multidisciplinaries: Mathematics

This paper scrutinized the impact of isothermal quartic autocatalytic form of chemical reaction have on a ternary hybrid nanofluid. In view of the nature of chemical reaction that is to take place in the system, a sizeable amount of heat is to be generated into the system, which will have an influence on some of the fluid properties. As such, fluid viscosity and thermal conductivity were considered to be temperature dependent. The ternary hybrid nanofluid was prepared by injecting ternary nanoparticles (Al2O3, SiO2 and Ag) into a non-Newtonian base fluid. The third-grade fluid model was …

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An Implementation Of The Method Of Moments On Chemical Systems With Constant And Time-Dependent Rates, Emmanuel O. Adara, Roger B. Sidje Sep 2023

An Implementation Of The Method Of Moments On Chemical Systems With Constant And Time-Dependent Rates, Emmanuel O. Adara, Roger B. Sidje

Northeast Journal of Complex Systems (NEJCS)

Among numerical techniques used to facilitate the analysis of biochemical reactions, we can use the method of moments to directly approximate statistics such as the mean numbers of molecules. The method is computationally viable in time and memory, compared to solving the chemical master equation (CME) which is notoriously expensive. In this study, we apply the method of moments to a chemical system with a constant rate representing a vascular endothelial growth factor (VEGF) model, as well as another system with time-dependent propensities representing the susceptible, infected, and recovered (SIR) model with periodic contact rate. We assess the accuracy of …

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(R1522) Modelling The Influence Of Desertic Aerosols On The Transmission Dynamics Of Neisseria Meningitidis Serogroup A, Francis Signing, Berge Tsanou, Samuel Bowong Dec 2022

(R1522) Modelling The Influence Of Desertic Aerosols On The Transmission Dynamics Of Neisseria Meningitidis Serogroup A, Francis Signing, Berge Tsanou, Samuel Bowong

Applications and Applied Mathematics: An International Journal (AAM)

This paper assesses the role of desert aerosols and vaccine on the transmission dynamics of Neisseria Meningitis serogroup A (NmA). It is biologically well-documented that the inhalation of aerosol dust and its presence in the nasal cavity weakens the nasopharyngeal mucosa by damaging the mucosal barrier and inhibiting the mucosal immune defenses of susceptible and vaccinated individuals. We address the latter by proposing and analyzing a mathematical model for the dynamics of NmA that specifically accounts for the fast progression of susceptible and vaccinated individuals to the invasive stage of the disease. We compute the basic reproduction number and use …

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(Si10-057) Effect Of Time-Delay On An Sir Type Model For Infectious Diseases With Saturated Treatment, R. P. Gupta, Arun Kumar Oct 2022

(Si10-057) Effect Of Time-Delay On An Sir Type Model For Infectious Diseases With Saturated Treatment, R. P. Gupta, Arun Kumar

Applications and Applied Mathematics: An International Journal (AAM)

This study presents the complex dynamics of an SIR epidemic model incorporating a constant time-delay in incidence rate with saturated type of treatment rate. The system is studied to observe the effect of time lag in the asymptotic stability of endemic equilibrium states. We also establish global asymptotic stability of both disease-free and endemic equilibrium states by Lyapunov direct method with the help of suitable Lyapunov functionals. The existences of periodic solutions are ensured for the suitable choice of delay parameter. Finally, we perform numerical simulations supporting the analytical findings as well as to observe the effect of time-delay. The …

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Maintaining Ecosystem And Economic Structure In A Three-Species Dynamical System In Chesapeake Bay, Maila Hallare, Iordanka Panayotova Jul 2022

Maintaining Ecosystem And Economic Structure In A Three-Species Dynamical System In Chesapeake Bay, Maila Hallare, Iordanka Panayotova

CODEE Journal

We consider a three-species fish dynamical system in Chesapeake Bay consisting of the Atlantic menhaden as the prey and its two competing predators, the striped bass and the catfish. Building on our previous work in this system, we consider the issue of balancing economic harvesting goals (financial gain for fishermen) with ecological harvesting goals (non-extinction of species). In particular, we investigate the bionomic equilibria, maximum sustainable yield, and the maximum economic yield. Analytical computations and numerical simulations are employed to provide some mathematical guidance on fisheries management policies.

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(R1889) Analysis Of Resonant Curve In The Earth-Moon System Under The Effect Of Resistive Force And Earth’S Equatorial Ellipticity, Sushil Yadav, Mukesh Kumar, Rajiv Aggarwal Jun 2022

(R1889) Analysis Of Resonant Curve In The Earth-Moon System Under The Effect Of Resistive Force And Earth’S Equatorial Ellipticity, Sushil Yadav, Mukesh Kumar, Rajiv Aggarwal

Applications and Applied Mathematics: An International Journal (AAM)

In the present paper, we have determined the equations of motion of the Moon in spherical coordinate system using the gravitational potential of Earth. Using perturbation, equations of motion are reduced to a second order differential equation. From the solution, two types of resonance are observed: (i) due to the frequencies–rate of change of Earth’s equatorial ellipticity parameter and Earth’s rotation rate, and (ii) due to the frequencies–angular velocity of the bary-center around the sun and Earth’s rotation rate. Resonant curves are drawn where oscillatory amplitude becomes infinitely large at the resonant points. The effect of Earth’s equatorial ellipticity parameter …

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Analysis Of Sir Epidemic Models With Sociological Phenomenon, Robert F. Allen, Katherine C. Heller, Matthew A. Pons Mar 2022

Analysis Of Sir Epidemic Models With Sociological Phenomenon, Robert F. Allen, Katherine C. Heller, Matthew A. Pons

Spora: A Journal of Biomathematics

We propose two SIR models which incorporate sociological behavior of groups of individuals. It is these differences in behaviors which impose different infection rates on the individual susceptible populations, rather than biological differences. We compute the basic reproduction number for each model, as well as analyze the sensitivity of R0 to changes in sociological parameter values.

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Controlling And Synchronizing Combined Effect Of Chaos Generated In Generalized Lotka-Volterra Three Species Biological Model Using Active Control Design, Taqseer Khan, Harindri Chaudhary Dec 2020

Controlling And Synchronizing Combined Effect Of Chaos Generated In Generalized Lotka-Volterra Three Species Biological Model Using Active Control Design, Taqseer Khan, Harindri Chaudhary

Applications and Applied Mathematics: An International Journal (AAM)

In this work, we study hybrid projective combination synchronization scheme among identical chaotic generalized Lotka-Volterra three species biological systems using active control design. We consider here generalized Lotka-Volterra system containing two predators and one prey population existing in nature. An active control design is investigated which is essentially based on Lyapunov stability theory. The considered technique derives the global asymptotic stability using hybrid projective combination synchronization technique. In addition, the presented simulation outcomes and graphical results illustrate the validation of our proposed scheme. Prominently, both the analytical and computational results agree excellently. Comparisons versus others strategies exhibiting our proposed technique …

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Bifurcation Analysis For Prey-Predator Model With Holling Type Iii Functional Response Incorporating Prey Refuge, Lazaar Oussama, Mustapha Serhani Dec 2019

Bifurcation Analysis For Prey-Predator Model With Holling Type Iii Functional Response Incorporating Prey Refuge, Lazaar Oussama, Mustapha Serhani

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we carried out the bifurcation analysis for a Lotka-Volterra prey-predator model with Holling type III functional response incorporating prey refuge protecting a constant proportion of the preys. We study the local bifurcation considering the refuge constant as a parameter. From the center manifold equation, we establish a transcritical bifurcation for the boundary equilibrium. In addition, we prove the occurrence of Hopf bifurcation for the homogeneous equilibrium. Moreover, we give the radius and period of the unique limit cycle for our system

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Qualitative Analysis Of A Modified Leslie-Gower Predator-Prey Model With Weak Allee Effect Ii, Manoj K. Singh, B. S. Bhadauria Jun 2019

Qualitative Analysis Of A Modified Leslie-Gower Predator-Prey Model With Weak Allee Effect Ii, Manoj K. Singh, B. S. Bhadauria

Applications and Applied Mathematics: An International Journal (AAM)

The article aims to study a modified Leslie-Gower predator-prey model with Allee effect II, affecting the functional response with the assumption that the extent to which the environment provides protection to both predator and prey is the same. The model has been studied analytically as well as numerically, including stability and bifurcation analysis. Compared with the predator-prey model without Allee effect, it is found that the weak Allee effect II can bring rich and complicated dynamics, such as the model undergoes to a series of bifurcations (Homoclinic, Hopf, Saddle-node and Bogdanov-Takens). The existence of Hopf bifurcation has been shown for …

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Resonance In The Motion Of A Geocentric Satellite Due To Poynting-Robertson Drag And Equatorial Ellipticity Of The Earth, Charanpreet Kaur, Binay K. Sharma, Sushil Yadav Jun 2019

Resonance In The Motion Of A Geocentric Satellite Due To Poynting-Robertson Drag And Equatorial Ellipticity Of The Earth, Charanpreet Kaur, Binay K. Sharma, Sushil Yadav

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the problem of resonance in a motion of a geocentric satellite is numerically investigated under the consolidated gravitational forces of the Sun, the Earth including Earth’s equatorial ellipticity parameter and Poynting-Robertson (P-R) drag. We are presuming that bodies lying on an ecliptic plane are the Sun and the Earth, and satellite on orbital plane. Resonance is monitored between satellite’s mean motion and average angular velocity of the Earth around the Sun, and also between satellite’s mean motion and equatorial ellipticity parameter of the Earth. We also perform a systematic and thorough analysis in an attempt to understand …

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Resonance In The Motion Of A Geocentric Satellite Due To Poynting-Robertson Drag, Charanpreet Kaur, Binay K. Sharma, L. P. Pandey Jun 2018

Resonance In The Motion Of A Geocentric Satellite Due To Poynting-Robertson Drag, Charanpreet Kaur, Binay K. Sharma, L. P. Pandey

Applications and Applied Mathematics: An International Journal (AAM)

The problem of resonance in a geocentric Satellite under the combined gravitational forces of the Sun and the Earth due to Poynting-Robertson (P-R) drag has been discussed in this paper with the assumption that all three bodies, the Earth, the Sun and the Satellite, lie in an ecliptic plane. Our approach differs from conventional ones as we have placed evaluated velocity of the Satellite in equations of motion.We observed five resonance points commensurable between the mean motion of the Satellite and the average angular velocity of the Earth around the Sun, out of which two resonances occur only due to …

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A Mathematical Study For The Existence And Survival Of Human Population In A Polluted Environment, Manju Agarwal, Preeti _ Jun 2018

A Mathematical Study For The Existence And Survival Of Human Population In A Polluted Environment, Manju Agarwal, Preeti _

Applications and Applied Mathematics: An International Journal (AAM)

Rapidly rising population and increasing urbanization have the potential for producing a high level of pollution. Pollutants have the ability to change the distributions of patterns of plants and animals. Some of the main pollutant categories are water pollutants, air pollution, pesticides, and radioactive waste. Most abundantly toxicants are produced by the chemical and medical industries. We used food crops that are produced by using pesticide and herbicides, etc. Due to the enormous variety of toxic substances are present in the atmosphere, it is challenging task to determine the potential ecological and human health risk. Keeping all these things in …

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On The Lp-Spaces Techniques In The Existence And Uniqueness Of The Fuzzy Fractional Korteweg-De Vries Equation’S Solution, F. Farahrooz, A. Ebadian, S. Najafzadeh Dec 2017

On The Lp-Spaces Techniques In The Existence And Uniqueness Of The Fuzzy Fractional Korteweg-De Vries Equation’S Solution, F. Farahrooz, A. Ebadian, S. Najafzadeh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, is proposed the existence and uniqueness of the solution of all fuzzy fractional differential equations, which are equivalent to the fuzzy integral equation. The techniques on LP-spaces are used, defining the LpF F ([0; 1]) for 1≤P≤∞, its properties, and using the functional analysis methods. Also the convergence of the method of successive approximations used to approximate the solution of fuzzy integral equation be proved and an iterative procedure to solve such equations is presented.

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Numerical Simulation Of The Phase Space Of Jupiter-Europa System Including The Effect Of Oblateness, Vinay Kumar, Beena R. Gupta, Rajiv Aggarwal Jun 2017

Numerical Simulation Of The Phase Space Of Jupiter-Europa System Including The Effect Of Oblateness, Vinay Kumar, Beena R. Gupta, Rajiv Aggarwal

Applications and Applied Mathematics: An International Journal (AAM)

We have numerically investigated the phase space of the Jupiter-Europa system in the framework of a Circular Restricted Three-Body Problem. In our model, Jupiter is taken as oblate primary. We have considered time-frequency analysis (TFA) based on wavelets and the Poincare Surface of Section (PSS) for the characterization of orbits in the Jupiter-Europa model. We have exploited both cases: a system with and without considering the effect of oblateness. Graphs (ridge-plots) explaining the phenomenon of resonance trapping, a difference between chaotic sticky orbit and the non-sticky orbit, and periodic and quasi-periodic orbit are presented. Our results of Poincare surfaces of …

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Controllability Of An Eco-Epidemiological System With Disease Transmission Delay: A Theoretical Study, Samadyuti Haldar, Kunal Chakraborty, T. K. Kar Jun 2015

Controllability Of An Eco-Epidemiological System With Disease Transmission Delay: A Theoretical Study, Samadyuti Haldar, Kunal Chakraborty, T. K. Kar

Applications and Applied Mathematics: An International Journal (AAM)

This paper deals with the qualitative analysis of a disease transmission delay induced prey preda-tor system in which disease spreads among the predator species only. The growth of the preda-tors’ susceptible and infected subpopulations is assumed as modified Leslie–Gower type. Suffi-cient conditions for the persistence, permanence, existence and stability of equilibrium points are obtained. Global asymptotic stability of the system is investigated around the coexisting equilib-rium using a geometric approach. The existence of Hopf bifurcation phenomenon is also exam-ined with respect to some important parameters of the system. The criterion for disease a trans-mission delay the induced Hopf bifurcation phenomenon …

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Improving Airplane Touchdown Control By Utilizing The Adverse Elevator Effect, Nihad E. Daidzic Ph.D., Sc.D. Oct 2014

Improving Airplane Touchdown Control By Utilizing The Adverse Elevator Effect, Nihad E. Daidzic Ph.D., Sc.D.

International Journal of Aviation, Aeronautics, and Aerospace

The main objective of this original research article is to understand the short-term dynamic behavior of the transport-category airplane during landing flare elevator control application. Increasing the pitch angle to arrest the sink rate, the elevator will have to produce negative lift to rotate the airplane’s nose upward. This has an immediate adverse effect of initially accelerating airplane downward. A mathematical model of landing flare based on the flat-Earth longitudinal dynamics of rigid airplane was developed which is realistic only on very short time-scales as pitch stiffness and damping were neglected. Pilot control scenarios using impulse and step elevator pull-up …

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Global Dynamics Of A Water-Borne Disease Model With Multiple Transmission Pathways, Prasanta K. Mondal, T. K. Kar Jun 2013

Global Dynamics Of A Water-Borne Disease Model With Multiple Transmission Pathways, Prasanta K. Mondal, T. K. Kar

Applications and Applied Mathematics: An International Journal (AAM)

We propose and analyze a water born disease model introducing water-to-person and person-toperson transmission and saturated incidence. The disease-free equilibrium and the existence criterion of endemic equilibrium are investigated. Trans critical bifurcation at the disease-free equilibrium is obtained when the basic reproductive number is one. The local stability of both the equilibria is shown and a Lyapunov functional approach is also applied to explore the global stability of the system around the equilibria. We display the effects of pathogen contaminated water and infection through contact on the system dynamics in the absence of person-to-person contact as well as in the …

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