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 No-Equilibrium Hyperchaotic System and Its Fractional-Order Form

No-equilibrium system with chaotic behavior has attracted considerable attention recently because of its hidden attractor. We study a new four-dimensional system without equilibrium in this work. The new no-equilibrium system exhibits hyperchaos and coexisting attractors. Amplitude control feature of the system is also discovered. The commensurate fractional-order version of the proposed system is studied using numerical simulations. By tuning the commensurate fractional-order, the proposed system displays a wide variety of dynamical behaviors ranging from coexistence of quasiperiodic and chaotic attractors and bistable chaotic attractors to point attractor via transient chaos

Analysis of Josephson junction with topologically nontrivial barrier

Josephson junction (JJ) with topologically nontrivial barrier is analytically and numerically analyzed in this paper. This system has four, two, or no equilibrium points depending on the external direct current (DC) source and the fractional parameter. The existence of pitchfork bifurcation is established during the stability analysis of the equilibrium points. The inclusion of fractional parameter in JJ leads to an increase in the hysteresis loop of current-voltage characteristics. For a suitable choice of modulation parameters of external current source, JJ with topologically nontrivial barrier can display excitable mode, bistable, periodic and chaotic behaviors

Dynamic analysis, FPGA implementation, and cryptographic application of an autonomous 5D chaotic system with offset boosting

An autonomous five-dimensional (5D) system with offset boosting is constructed by modifying the well-known three-dimensional autonomous Liu and Chen system. Equilibrium points of the proposed autonomous 5D system are found and its stability is analyzed. The proposed system includes Hopf bifurcation, periodic attractors, quasi-periodic attractors, a one-scroll chaotic attractor, a double-scroll chaotic attractor, coexisting attractors, the bistability phenomenon, offset boosting with partial amplitude control, reverse period-doubling, and an intermittency route to chaos. Using a field programmable gate array (FPGA), the proposed autonomous 5D system is implemented and the phase portraits are presented to check the numerical simulation results. The chaotic attractors and coexistence of the attractors generated by the FPGA implementation of the proposed system have good qualitative agreement with those found during the numerical simulation. Finally, a sound data encryption and communication system based on the proposed autonomous 5D chaotic system is designed and illustrated through a numerical example

Pitchfork and Hopf bifurcations in quantum dot light emitting diode: analysis and prediction by using artificial neural network

The analytical and numerical analyses as well as prediction with artificial neural network (ANN) for chaos-based artificial intelligence applications of quantum dot light emitting diode (QDLED) are investigated in this paper. The system of equations describing QDLED has three, or one equilibrium points depending on the capture rate from wetting layer into the dot and the injection current. The stability analysis of the equilibrium points reveals the existence of Pitchfork and Hopf bifurcations. The different dynamical behaviors (including steady state, periodic and chaotic behaviors) found in QDLED are illustrated in two parameters bifurcation diagrams, phase portraits and time series. Finaly, the QDLED system is predicted using ANN for chaos-based artificial intelligence applications

Microcontroller Implementation, Chaos Control, Synchronization and Antisynchronization of Josephson Junction Model

The microcontroller implementation, chaos control, synchronization, and antisynchronization of the nonlinear resistive-capacitive-inductive shunted Josephson junction (NRCISJJ) model are reported in this paper. The dynamical behavior of the NRCISJJ model is performed using phase portraits, and time series. The numerical simulation results reveal that the NRCISJJ model exhibits different shapes of hidden chaotic attractors by varying the parameters. The existence of different shapes of hidden chaotic attractors is confirmed by microcontroller results obtained from the microcontroller implementation of the NRCISJJ model. It is theoretically demonstrated that the two designed single controllers can suppress the hidden chaotic attractors found in the NRCISJJ model. Finally, the synchronization and antisynchronization of unidirectional coupled NRCISJJ models are studied by using the feedback control method.  Thanks to the Routh Hurwitz stability criterion, the controllers are designed in order to control chaos in JJ models and achieved synchronization and antisynchronization between coupled NRCISJJ models. Numerical simulations are shown to clarify and confirm the control, synchronization, and antisynchronization

Direct modulation of semiconductor ring lasers: numerical and asymptotic analysis

info:eu-repo/semantics/publishe

Analysis and FPGA implementation of an autonomous Josephson junction snap oscillator

An autonomous Josephson junction (JJ) snap oscillator is designed and investigated in this paper. Depending on DC bias current, the proposed snap oscillator has two or no equilibrium points. The stability analysis of the two equilibrium points shows that one of the equilibrium point is unstable and the existence of Hopf bifurcation is established for the other equilibrium point. During the numerical analysis, some interesting dynamical behaviors such as chaotic self-excited attractors, chaotic hidden attractors, antimonotonicity, chaotic bubble hidden attractors, bistable period-1-bubble and coexistence between periodic and chaotic hidden attractors are found. Finally, the Field Programmable Gate Array (FPGA) of proposed snap oscillator is implemented. The results obtained from the FPGA implementation of proposed snap oscillator are qualitatively the same to the one obtained during the numerical simulations