Dynamics of the Forced Thirring Instanton with Two Forcing Terms

We consider the dynamical behavior of fermionic instanton solutions of the Thirring Model with two forcing terms. In particular, the study focuses on the effect of the frequency and amplitude of the forcing terms on the behavior of fermionic instanton solutions. Numerical analysis based on the Smaller Alignment Index (SALI) method, Bifurcation Diagram and Permutation Entropy (PE) are used to show how and which dynamical behaviors occur in the system. Color maps and diagrams of the SALI time (St) (the time St required for the SALI index to below a threshold value of 10−12) and PE of the system with respect to varying of frequency and amplitude values of the forcing terms are plotted comparatively to determine different dynamical behavior of the system. The study shows that fermionic instanton solutions exhibit a wide variety of dynamical behavior due to two forcing terms. Furthermore, it is emphasized that SALI time (St) can be easily compared with bifurcation diagram and complexity method as a fast, efficient and precise method to investigate different degrees of chaos. In general, the instanton solutions with two forcing terms have been observed to exhibit different type of dynamical behavior. In this study, identical and symmetric coexisting attractors are demonstrated for these different types of behavior of the forced Thirring instanton.