Azad Ibrahim Amen

Salahaddin University - Erbil | SUH · Department of Mathematics

In this study, we investigate the integrability and linearizability problems of a family of cubic three-dimensional Lotka–Volterra systems with one zero eigenvalue, involving seventeen parameters. Necessary conditions on the parameters of the system for both integrability and linearizability are obtained by computing the resonant quantities using G...

In this paper, we investigate a quadratic chaotic system modeling self-excited and hidden attractors which is described by a system of three nonlinear ordinary differential equations with three real parameters. The primary goal is to establish the existence of two limit cycles that bifurcate based on the system’s nature as an electronic circuits mo...

Numerous recently introduced chaotic systems exhibit straightforward algebraic representations. In this study, we explore the potential for identifying a global analytic first integral in a generalized 3-dimensional chaotic system (2). Our work involves detailing the model of a new 3-D chaotic system characterized by three Lyapunov exponents—positi...

In this study, the quadratic 3-dimensional differential system is considered, in which the origin of the coordinate becomes the Hopf equilibrium point. The existence and stability of limit cycles that emerge from the Hopf point are being investigated. The Lyapunov coefficients connected to the Hopf point are calculated using the projection method....

In this paper, integrability and the global dynamics of two chaotic systems, Coullet and Malasoma systems, are studied. We mainly use the contradiction technique to show that both systems have no polynomial, Darboux and rational first integrals. Moreover, it is proved that the Cullet system has no analytic first integrals if some conditions on the...

The aim of this study is to analyze the integrability problem of Lotka--Volterra three species biological system. The system which considered in this work is a biological plausibility or a chemical model. The system has a complex dynamical behavior because it is chaotic system. We, first show that the system is a complete integrable when two of the...

In this work periodic solutions of a three dimensional chaos laser system, which externallyinjected class ff which is described by a system of three nonlinear ordinary differential equationswith two parameters for field intensity phase and population inversion, are studied. The firstorder of the method of averaging theory is applied for determine a...

We study the dynamics of a version of the Jaynes–Cummings system without the rotating wave approximation, which essentially consists of the interaction of two systems, n$$ n $$ two‐level atoms and a single system of electromagnetic field. In particular, we investigate some types of first integrals such as Darboux, analytic, and time‐dependent first...

In this paper the complex dynamics of a smallest biochemical system model in three-dimensional systems with the reaction scheme. This model is described by a system of three nonlinear ordinary differential equations with five positive real parameters, are analyzed and studied. We present a thorough analysis of their invariant algebraic surfaces and...

We focus on a chaotic differential system in 3-dimension, including an absolute term and a line of equilibrium points. Which describes in the following ẋ = y , ẏ = −ax + yz , ż = by − cxy − x². This system has an implementation in electronic components. The first purpose of this paper is to provide sufficient conditions for the existence of a limit...

This work aims to analyse the dynamic behaviours of the forest pest system. We confirm the forest pest system in plane for limit cycles bifurcating existence from a Hopf bifurcation under certain conditions by using the first Lyapunov coefficient and the second-order of averaging theory. It is shown that all stationary points in this system have Ho...

We focus on a chaotic differential system in 3-dimension, including an absolute term and a line of equilibrium points. Which describes in the following This system has an implementation in electronic components. The first purpose of this paper is to provide sufficient conditions for the existence of a limit cycle bifurcating from the zeroHopf equil...

In this paper, the first integrals of Darboux type of the generalized Sprott ET9 chaotic system will be studied. This study showed that the system has no polynomial, rational, analytic and Darboux first integrals for any value of . All the Darboux polynomials for this system were derived together with its exponential factors. Using the weight homog...

In this work, we focus on studying the integrability of the following three-dimensional Van der Pol–Duffing system x ˙ = − m ( x 3 − μ x − y ) , y ˙ = x − y − z , z ˙ = β y . More precisely, if m β ≠ 0, then the above system has no analytic and nor Darboux first integrals at the neighborhood of the origin. Also, the stability and instability of the...

In this paper, we investigate the first integrals of the following system ̇ ̇ ̇ where and ,. This kind of system is a special case of three-dimensional polynomial cubic differential systems. Generally, several methods can be used to investigate the first integrals, but unfortunately, most of them are not enabled for finding first integrals. In this...

We provide necessary and sufficient conditions for both integrability and linearizability of a three dimensional vector field with quadratic nonlinearities. For our investigation we consider the case of (1:−2:1)–resonance at the origin and in general non of the axes planes is invariant. Hence, we deal with a nine parametric family of quadratic syst...

In this paper, we study the first integrals of Darboux type of the differential system x˙=y,y˙=−x+yz,z˙=−x−axy−bxz, which exhibits chaotic phenomena for suitable chosen values of the real parameters a and b. We show that the system has no polynomial, rational, or Darboux first integrals for any value of a and b. All the Darboux polynomials of the s...

We investigate the global stability, existence and nonexistence of limit cycles of general Sel’kov model using different approach such as qualitative analysis, Dulac’s criterion, Lyapunov function and Poincaré-Bendixson theorem. We also study the nonexistence of analytic first integrals of the general Sel’kov model.

We investigate the global stability, existence and nonexistence of limit cycles of general Sel’kov model using different approach such as qualitative analysis, Dulac’s criterion, Lyapunov function and Poincaré-Bendixson theorem. We also study the nonexistence of analytic first integrals of the general Sel'kov model.

A zero-Hopf equilibrium in a three-dimensional system is an isolated equilibrium point which has a zero eigenvalue and a simple pair of purely imaginary eigenvalues. In general, for such an equilibrium, there is no theory for finding when some periodic solutions are bifurcated by perturbing the parameters of the system. In this work, we describe th...

The main aim of this paper is to construct Bendixson-Dulac and Dulac-Cherkas functions to study the maximum number of limit cycles for several families of planar dynamical system. We also apply the results to Lienard and biochemistry reaction systems.

A new condition is given for generalized Abel differential equation to have a center. We apply the results to some polynomial differential systems in the plane to find necessary and sufficient center conditions.

We prove that near the bifurcation point unstable limit cycle arises from the Lorenz system. In the analysis, we use the method of local bifurcation theory, especially the center manifold and the normal form theorem. A computer algebra system using Maple to derive all the formulas and verify the results presented in this paper.

W. H. Aziz and. Multiplicity of Periodic Solutions by Word Problems, J. Zanco. Pure & Applied Scince, Salahaddin University, V 16, No.1 (2004),73-82.