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Applied Mathematics Commons™

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Ordinary Differential Equations and Applied Dynamics

Prairie View A&M University

2022

Articles 1 - 16 of 16

Full-Text Articles in Applied Mathematics

(R1969) On The Approximation Of Eventual Periodicity Of Linearized Kdv Type Equations Using Rbf-Ps Method, Hameed Ullah Jan, Marjan Uddin, Asma Norin, Tamheeda . Dec 2022

(R1969) On The Approximation Of Eventual Periodicity Of Linearized Kdv Type Equations Using Rbf-Ps Method, Hameed Ullah Jan, Marjan Uddin, Asma Norin, Tamheeda .

Applications and Applied Mathematics: An International Journal (AAM)

Water wave propagation phenomena still attract the interest of researchers from many areas and with various objectives. The dispersive equations, including a large body of classes, are widely used models for a great number of problems in the fields of physics, chemistry and biology. For instance, the Korteweg-de Vries (KdV) equation is one of the famous dispersive wave equation appeared in the theories of shallow water waves with the assumption of small wave-amplitude and large wave length, also its various modifications serve as the modeling equations in several physical problems. Another interesting qualitative characteristic of solutions of some dispersive wave …

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(R2020) Dynamical Study And Optimal Harvesting Of A Two-Species Amensalism Model Incorporating Nonlinear Harvesting, Manoj Kumar Singh, Poonam . Dec 2022

(R2020) Dynamical Study And Optimal Harvesting Of A Two-Species Amensalism Model Incorporating Nonlinear Harvesting, Manoj Kumar Singh, Poonam .

Applications and Applied Mathematics: An International Journal (AAM)

This study proposes a two-species amensalism model with a cover to protect the first species from the second species, with the assumption that the growth of the second species is governed by nonlinear harvesting. Analytical and numerical analyses have both been done on this suggested ecological model. Boundedness and positivity of the solutions of the model are examined. The existence of feasible equilibrium points and their local stability have been discussed. In addition, the parametric conditions under which the proposed system is globally stable have been determined. It has also been shown, using the Sotomayor theorem, that under certain parametric …

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(R1980) Effect Of Climate Change On Brain Tumor, Pardeep Kumar, Sarita Jha, Rajiv Aggarwal, Govind Kumar Jha Dec 2022

(R1980) Effect Of Climate Change On Brain Tumor, Pardeep Kumar, Sarita Jha, Rajiv Aggarwal, Govind Kumar Jha

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we introduce a new dynamical model addressing the variation in climate condition due the presence of microorganisms. We also introduce a new dynamical model of cancer growth which includes three interactive cell populations with drug free environment, namely tumor cells, healthy host cells, and immune effector cells. In this, we considered the super growth of tumor cells. For the choice of certain parameters, both of the systems exhibit chaotic behavior. The aim of this work is to design the controller to control the chaos and to provide sufficient conditions which achieve synchronization of two non-identical systems, which …

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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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(R1888) On The Mackey-Glass Model With A Piecewise Constant Argument, Mehtap Lafci Büyükkahraman Dec 2022

(R1888) On The Mackey-Glass Model With A Piecewise Constant Argument, Mehtap Lafci Büyükkahraman

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we deal with the Mackey-Glass model with piecewise constant argument. Because the corresponding difference equation is the difference solution of the equation, the difference equation can clearly predict the dynamic behavior of the equation. So, we look at how the difference equation behaves.We study the asymptotic stability of the equilibrium point of the difference equation and it is obtained that this point is a repeller under some conditions. Also, it is shown that every oscillatory solution of the difference equation has semi-cycles of length at least two, and every oscillatory solution of the difference equation is attracted …

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(R1992) Rbf-Ps Method For Eventual Periodicity Of Generalized Kawahara Equation, Hameed Ullah Jan, Marjan Uddin, Arif Ullah, Naseeb Ullah Dec 2022

(R1992) Rbf-Ps Method For Eventual Periodicity Of Generalized Kawahara Equation, Hameed Ullah Jan, Marjan Uddin, Arif Ullah, Naseeb Ullah

Applications and Applied Mathematics: An International Journal (AAM)

In engineering and mathematical physics, nonlinear evolutionary equations play an important role. Kawahara equation is one of the famous nonlinear evolution equation appeared in the theories of shallow water waves possessing surface tension, capillary-gravity waves and also magneto-acoustic waves in a plasma. Another specific subjective parts of arrangements for some of evolution equations evidenced by findings link belonging to their long-term actions named as eventual time periodicity discovered over solutions to IBVPs (initial-boundary-value problems). Here we investigate the solution’s eventual periodicity for generalized fifth order Kawahara equation (IBVP) on bounded domain in combination with periodic boundary conditions numerically exploiting mesh-free …

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(Si10-123) Comparison Between The Homotopy Perturbation Method And Variational Iteration Method For Fuzzy Differential Equations, P. Chandru, B. Radhakrishnan Oct 2022

(Si10-123) Comparison Between The Homotopy Perturbation Method And Variational Iteration Method For Fuzzy Differential Equations, P. Chandru, B. Radhakrishnan

Applications and Applied Mathematics: An International Journal (AAM)

In this article, the authors discusses the numerical simulations of higher-order differential equations under a fuzzy environment by using Homotopy Perturbation Method and Variational Iteration Method. The fuzzy parameter and variables are represented by triangular fuzzy convex normalized sets. Comparison of the results are obtained by the homotopy perturbation method with those obtained by the variational iteration method. Examples are provided to demonstrate the theory.

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(Si10-083) Approximate Controllability Of Infinite-Delayed Second-Order Stochastic Differential Inclusions Involving Non-Instantaneous Impulses, Shobha Yadav, Surendra Kumar Oct 2022

(Si10-083) Approximate Controllability Of Infinite-Delayed Second-Order Stochastic Differential Inclusions Involving Non-Instantaneous Impulses, Shobha Yadav, Surendra Kumar

Applications and Applied Mathematics: An International Journal (AAM)

This manuscript investigates a broad class of second-order stochastic differential inclusions consisting of infinite delay and non-instantaneous impulses in a Hilbert space setting. We first formulate a new collection of sufficient conditions that ensure the approximate controllability of the considered system. Next, to investigate our main findings, we utilize stochastic analysis, the fundamental solution, resolvent condition, and Dhage’s fixed point theorem for multi-valued maps. Finally, an application is presented to demonstrate the effectiveness of the obtained results.

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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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(Si10-056) Fear Effect In A Three Species Prey-Predator Food-Web System With Harvesting, R. P. Gupta, Dinesh K. Yadav Oct 2022

(Si10-056) Fear Effect In A Three Species Prey-Predator Food-Web System With Harvesting, R. P. Gupta, Dinesh K. Yadav

Applications and Applied Mathematics: An International Journal (AAM)

Some recent studies and field experiments show that predators affect their prey not only by direct capture; they also induce fear in prey species, which reduces their reproduction rate. Considering this fact, we propose a mathematical model to study the fear effect of a middle predator on its prey in a three-species food web system with harvesting. The ecological feasibility of solutions to the proposed system is guaranteed in terms of positivity and boundedness. The local stability of stationary points in the proposed system is derived. Multiple co-existing stationary points for the proposed system are observed, which makes the problem …

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(Si10-115) Controllability Results For Nonlinear Impulsive Functional Neutral Integrodifferential Equations In N-Dimensional Fuzzy Vector Space, Murugesan Nagarajan, Kumaran Karthik Oct 2022

(Si10-115) Controllability Results For Nonlinear Impulsive Functional Neutral Integrodifferential Equations In N-Dimensional Fuzzy Vector Space, Murugesan Nagarajan, Kumaran Karthik

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we concentrated to study the controllability of fuzzy solution for nonlinear impulsive functional neutral integrodifferential equations with nonlocal condition in n-dimensional vector space. Moreover, we obtained controllability of fuzzy result for the normal, convex, upper semi-continuous and compactly supported interval fuzzy number. Finally, an example was provided to reveal the application of the result.

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(R1892) On The Asymptotic Stability Of A Neutral System With Nonlinear Perturbations And Constant Delay, Melek Gözen Jun 2022

(R1892) On The Asymptotic Stability Of A Neutral System With Nonlinear Perturbations And Constant Delay, Melek Gözen

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we consider a nonlinear perturbed system of neutral delay integro-differential equations (NDIDEs). We prove two new theorems, Theorems 1 and 2, such that these theorems include sufficient conditions and are related to asymptotically stability of zero solution of the perturbed system of NDIDEs. The technique of the proofs depend upon the definitions of two new and more suitable Lyapunov- Krasovskiĭ functionals (LKFs). When we compared the results of this paper with those are found the literature related , our results improve and extend some classical results, and do new contributions to the topic of NDIDEs and literature.

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(R1517) Asymptotical Stability Of Riemann-Liouville Fractional Neutral Systems With Multiple Time-Varying Delays, Erdal Korkmaz, Abdulhamit Ozdemir Jun 2022

(R1517) Asymptotical Stability Of Riemann-Liouville Fractional Neutral Systems With Multiple Time-Varying Delays, Erdal Korkmaz, Abdulhamit Ozdemir

Applications and Applied Mathematics: An International Journal (AAM)

In this manuscript, we investigate the asymptotical stability of solutions of Riemann-Liouville fractional neutral systems associated to multiple time-varying delays. Then, we use the linear matrix inequality (LMI) and the Lyapunov-Krasovskii method to obtain sufficient conditions for the asymptotical stability of solutions of the system when the given delays are time dependent and one of them is unbounded. Finally, we present some examples to indicate the efficacy of the consequences obtained.

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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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(R1897) Further Results On The Admissibility Of Singular Systems With Delays, Abdullah Yiğit, Cemil Tunç Jun 2022

(R1897) Further Results On The Admissibility Of Singular Systems With Delays, Abdullah Yiğit, Cemil Tunç

Applications and Applied Mathematics: An International Journal (AAM)

Admissibility problem for a kind of singular systems with delays is studied in this article. Firstly, given the singular system with delays is transformed into a neutral system with delays. Secondly, a new sufficient criterion is obtained on the stability of the new neutral system by aid of Wirtinger-based integral inequality, linear matrix inequality (LMI) method and meaningful Lyapunov-Krasovskii functionals (LKFs). This criterion is valid for both systems. At the end, Two numerical examples are given to illustrate the applicability of the obtained results using MATLAB-Simulink software. By this article, we extend and improve some results of the past literature.

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(R1511) Numerical Solution Of Differential Difference Equations Having Boundary Layers At Both The Ends, Raghvendra Pratap Singh, Y. N. Reddy Jun 2022

(R1511) Numerical Solution Of Differential Difference Equations Having Boundary Layers At Both The Ends, Raghvendra Pratap Singh, Y. N. Reddy

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, numerical solution of differential-difference equation having boundary layers at both ends is discussed. Using Taylor’s series, the given second order differential-difference equation is replaced by an asymptotically equivalent first order differential equation and solved by suitable choice of integrating factor and finite differences. The numerical results for several test examples are presented to demonstrate the applicability of the method.

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