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The present paper focuses on some classes of dynamical systems involving Hamilton–Poisson structures, while neglecting their chaotic behaviors. Based on this, the closed-form solutions are obtained. These solutions are derived using the Optimal Auxiliary Functions Method (OAFM). The impact of the physical parameters of the system is also investigated. Periodic orbits around the equilibrium points are performed. There are homoclinic or heteroclinic orbits and they are obtained in exact form. The dynamical system is reduced to a second-order nonlinear differential equation, which is analytically solved through the OAFM procedure. The influence of initial conditions on the system is explored, specifically regarding the presence of symmetries. A good agreement between the analytical and corresponding numerical results is demonstrated, reflecting the accuracy of the proposed method. A comparative analysis underlines the advantages of the OAFM compared with the iterative method. The results of this work encourage the study of dynamical systems with bi-Hamiltonian structure and similar properties as physical and biological problems.
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; Pop Nicolina 2
; Badarau Rodica 3 1 Department of Mathematics, Politehnica University of Timisoara, 300006 Timisoara, Romania; [email protected]
2 Department of Physical Foundations of Engineering, Politehnica University of Timisoara, 2 Vasile Parvan Blvd., 300223 Timisoara, Romania
3 Department of Mechanical Machines, Equipment and Transportation, Politehnica University of Timisoara, 1 Mihai Viteazul Blvd., 300222 Timisoara, Romania; [email protected]