Phase portraits and orbit wise dynamics solutions, quasi-periodic and chaotic behavior of heisenberg ferromagnetic spin chains mode

This work addresses the Heisenberg ferromagnetic spin chain model through a dynamical system framework. We explore the model's phase plane by transforming it into a dynamical system, yielding diverse phase portraits based on parametric conditions. On the basis of parametric conditions and phase diagrams, we construct four propositions for diverse solutions along all orbits. We obtain exact results permitting along every orbit of the phase diagrams of the mode. This study yields exact solutions encompassing smooth periodic, dark, bright periodic, singular wave, dark bell solitary, bright bell solitary, bright-dark solitary wave, subharmonic wave, exponentially increasing wave, and exponentially decreasing wave solutions. By tracing the trajectory of each phase portrait, we obtain a range of numerical solutions utilizing the fourth-order Runge-Kutta method. Quasi-periodic and chaotic natures of the model extract for additional forcing term of the mode. We also test sensitivity due to small change in initial conditions in the solution of the mode.