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Chaos classification in forced fermionic instanton solutions by the Generalized Alignment Index (GALI) and the largest Lyapunov exponent

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  • Canbaz, Beyrul

Abstract

Instantons play an important role in particle physics and cosmology. Fermion-like instanton solutions are obtained in the two-dimensional Thirring model via Heisenberg ansatz. In this study, chaotic behavior of the fermion-like instanton solutions with an external periodic force is investigated. The chaotic behavior is analyzed by performing a comparative numerical study of the time evolution of the largest Lyapunov exponent (LLE) and the Generalized Alignment Index of order 2 (GALI2) method. Diagram of the LLE and GALI2 time (TG) (the time TG needed for the GALI2 to become <10−12) of the system of two nonlinear ordinary differential equations corresponding the forced fermion like instanton solutions with respect to varying the parameters at different time units are plotted comparatively. Moreover, color plots of the LLEs and GALI2 time (TG) of the system in the phase space are analyzed with different initial conditions for different parameters. As a result of these analyzes, the fermionic instanton solutions with an external periodic force are regular, chaotic and weakly chaotic states for some parameters and initial conditions. In addition, using diagram and color plot of the GALI2 time (TG), which is considered as an indicator of the system's chaoticity strength, by adjusting the needed time for the GALI2 to become <10−12 can be an alternative method to the diagram and color plot of the LLE of system with respect to varying the parameters.

Suggested Citation

  • Canbaz, Beyrul, 2022. "Chaos classification in forced fermionic instanton solutions by the Generalized Alignment Index (GALI) and the largest Lyapunov exponent," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    • Handle: RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922008645
    DOI: 10.1016/j.chaos.2022.112685
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