Bifurcation analysis for mixed derivative nonlinear Schrödinger’s equation , \(\alpha \)-helix nonlinear Schrödinger’s equation and Zoomeron model

Bifurcation analysis is a powerful method for investigating the steady-state nonlinear dynamics of systems. There are software programmes that allow for the numerical continuation of steady-state solutions while the system’s parameters are changed. The aim of this manuscript is to deal a mixed derivative nonlinear Schrödinger’s equation (MD-NLSE), \(\alpha \)-helix NLSE and Zoomeron model utilising the bifurcation theory technique of dynamical systems. A mathematical method called bifurcation analysis is used to examine how a system behaves when a parameter is changed. It is used to examine how the behaviour of the system changes as one or more parameters are altered and to find critical values of the parameters that cause appreciable changes in the behaviour of the system. Bifurcations are places in parameter space when the system’s qualitative behaviour abruptly shifts. A system could, for instance, go from having a stable equilibrium to oscillating between two states when a parameter is increased. To investigate these changes and comprehend how the system’s behaviour would alter if the parameter is further altered, bifurcation analysis is performed. An example of a phase portrait is a plot of a dynamic system’s phase space, which graphically depicts the behaviour of the system. A two-dimensional depiction of the system’s variables on the x and y axes is a common way to depict the phase space, which is the space of all conceivable states of the system. The paths of the system are shown as curves or lines in the phase space in a phase picture. These paths show how the system has changed over time and may be used to examine the stability and behaviour of the system. Phase portraits are often employed in the study of the behaviour of complex systems in physics, engineering, and mathematics. Numerous systems, including mechanical systems, electrical circuits, chemical processes, and biological systems, may be studied using them. Researchers can learn more about a system’s dynamics and forecast how it will behave in various situations by looking at its phase picture.