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A generalized form of the autonomous Bonhoeffer-van der Pol (BVdP) system described by a second-order dynamical system with six independent parameters consistent with its optimal mathematical modeling, instead of three usually used, is investigated. Through its equivalent form, the generalized asymmetric van der Pol-Duffing (GAVdPD) system and the steady states of this system are derived. The analysis show that the system may exhibit one or three steady states when it is driven by an external constant impulse taken as a main control parameter. Domain ranges in which the system can function as well as monostable system as a bistable system are derived. In addition, by means of the theory of Hopf Bifurcation, it appears that there are large possibilities for the system to work as self-sustained oscillator, forced oscillator or other possibilities for which the system does not operate, indicating the richness of this generalized form of the BVdP system. Limit cycle solutions are derived at the neighboring of the Andronov-Hopf Bifurcation points even for large values of the asymmetric parameter. All these results are checked through numerical simulations. Applying these analytical investigations to the electronic circuit executing the dynamics of the basic BVdP system, two distinct working regimes are highlighted, depending on the magnitude of the capacitance with respect to a threshold value function of the characteristic parameters both of the self and of the nonlinear resistance. Through PSPICE simulations the accuracy of these analytical and numerical investigations have been confirmed.

In this paper, the recording media is considered as nanowire where Domain Wall (DW) can move when a charge pulse current or a current density is injected. Using domain wall Kink Soliton profile, we investigate dynamics of magnetic domain wall while relying on the Landau-Lifshitz-Gilbert equation that will simultaneously take into account the Spin Transfer Torque with adiabatic and non-adiabatic contribution, the Spin Orbit Torque with Spin Hall Effect plus Rashba effect, the applied external magnetic field and Dzyaloshinskii-Moriya interaction. The impact and the influence of all these micro-phenomena taken separately or simultaneously on the speed of domain wall propagation is observed through the analytical and numerical tools such as the collectives coordinates method and the fourth-order Runge-Kutta algorithm. This allows us to define the different propagation regimes of domain wall within the magnetic chain with different range of speed amount attained by domain wall during the propagation. In addition to the effects of applied magnetic field and the Spin Transfer Torque, we have also shown that the DMI interaction, Spin Hall Effect, Rashba effect and the Slonczewski effect can also significantly influence the stability of the wall during its propagation. According to a certain phenomenon, the speed of 400 m∕s is observed even that the normal propagation regime in those cases is very brief. In addition, to avoid the uncontrollable joule effect in the magnetic nanowire and to allow a better propagation of the wall under Spin Transfer Torque the current density would be around 10 8 A.m −2 .