Hopf bifurcation, antimonotonicity and amplitude controls in the chaotic Toda jerk oscillator: analysis, circuit realization and combination synchronization in its fractional-order form

In this paper, an autonomous Toda jerk oscillator is proposed and analysed. The autonomous Toda jerk oscillator is obtained by converting an autonomous two-dimensional Toda oscillator with an exponential nonlinear term to a jerk oscillator. The existence of Hopf bifurcation is established during the stability analysis of the unique equilibrium point. For a suitable choice of the parameters, the proposed autonomous Toda jerk oscillator can generate antimonotonicity, periodic oscillations, chaotic oscillations and bubbles. By introducing two additional parameters in the proposed autonomous Toda jerk oscillator, it is possible to control partially or totally the amplitude of its signals. In addition, electronic circuit realization of the proposed Toda jerk oscillator is carried out to confirm results found during numerical simulations. The commensurate fractional-order version of the proposed autonomous chaotic Toda jerk oscillator is studied using the stability theorem of fractional-order oscillators and numerical simulations. It is found that periodic oscillations and chaos exist in the fractional-order form of the proposed Toda jerk oscillator with order less than three. Finally, combination synchronization of two fractional-order proposed autonomous chaotic Toda jerk oscillators with another fractional-order proposed autonomous chaotic Toda jerk oscillator is analysed using the nonlinear feedback control method

A train of bright and dark-rogue wave solitons in a polariton fluid with inhomogeneous strength interaction

We solve using the similarity transformation method a one-dimensionless driven-dissipative nonlinear Schrödinger equation to explore the dynamics of the rogue wave solitons generated in a polariton fluid. Under resonant excitation, we predict the existence of the bright and the dark-rogue waves solitons by varying the external pump source parameter. By considering, a time periodic polariton–polariton interaction and adjusting its frequency, the rogue wave soliton trains occur in a polariton fluid. In addition we observe that, the amplitude of the pump power is responsible to the formation of a the train of the bright and the dark rogue waves solitons