Izvorni znanstveni članak
https://doi.org/10.1080/00051144.2019.1600109
Hopf bifurcation, antimonotonicity and amplitude controls in the chaotic Toda jerk oscillator: analysis, circuit realization and combination synchronization in its fractional-order form
Justin Roger Mboupda Pone
; Research Unit of Automation and Applied Computer, Electrical Engineering Department of IUT-FV of Bandjoun, University of Dschang, Dschang, Cameroon
Sifeu Takougang Kingni
; Department of Mechanical, Petroleum and Gas Engineering, Faculty of Mines and Petroleum Industries, University of Maroua, Maroua, Cameroon
Guy Richard Kol
; Department of Mechanical, Petroleum and Gas Engineering, Faculty of Mines and Petroleum Industries, University of Maroua, Maroua, Cameroon
Viet-Thanh Pham
; Nonlinear Systems and Applications, Faculty of Electrical & Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam
Sažetak
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.
Ključne riječi
Chaotic jerk oscillator; Hopf bifurcation; antimonotonicity; partial or total amplitude control; fractional-order form; combination synchronization
Hrčak ID:
239776
URI
Datum izdavanja:
20.5.2019.
Posjeta: 672 *