Actuating mechanical arms coupled to an array of FitzHugh–Nagumo neuron circuits

The paper is aimed at mimicking the motion of myriapods by using an array of mechanical arms coupled to an array of FitzHugh–Nagumo (FN) neuron circuits. The differential equation depicting the electromechanical system is achieved by using Kirchhoff’s and Newton’s laws. The system parameters are sensitive to the stability of the system as shown by numerical simulations such that for different ranges of the stimulation current, the array of the FN neuron circuit coupled to a single mechanical arm is either in the non-excitable state, excitable state or in the oscillatory state. For the values of the stimulation current in the excitable state, an action potential (AP) achieved produced an excitation greater enough to actuate significantly the mechanical leg. In the excitable state, the action of the magnetic signal on the single mechanical arm increases the amplitude of the instantaneous displacement of the legs. The array of the coupled electromechanical system in the excitable state produces an AP for the different values of the legs having the same behavior as shown by numerical simulations, which implied that neurons communicate without loss of amplitude when in the permanent regime. This behavior is similar to the instantaneous displacement of the mechanical legs, hence depicting the straightforward motion of myriapods without rotation. Finally, the velocities of the propagation of nerve impulses and that of the displacement of legs are quantitatively the same

Analysis of a No Equilibrium Linear Resistive-Capacitive-Inductance Shunted Junction Model, Dynamics, Synchronization, and Application to Digital Cryptography in Its Fractional-Order Form

A linear resistive-capacitive-inductance shunted junction (LRCLSJ) model obtained by replacing the nonlinear piecewise resistance of a nonlinear resistive-capacitive-inductance shunted junction (NRCLSJ) model by a linear resistance is analyzed in this paper. The LRCLSJ model has two or no equilibrium points depending on the dc bias current. For a suitable choice of the parameters, the LRCLSJ model without equilibrium point can exhibit regular and fast spiking, intrinsic and periodic bursting, and periodic and chaotic behaviors. We show that the LRCLSJ model displays similar dynamical behaviors as the NRCLSJ model. Moreover the coexistence between periodic and chaotic attractors is found in the LRCLSJ model for specific parameters. The lowest order of the commensurate form of the no equilibrium LRCLSJ model to exhibit chaotic behavior is found to be 2.934. Moreover, adaptive finite-time synchronization with parameter estimation is applied to achieve synchronization of unidirectional coupled identical fractional-order form of chaotic no equilibrium LRCLSJ models. Finally, a cryptographic encryption scheme with the help of the finite-time synchronization of fractional-order chaotic no equilibrium LRCLSJ models is illustrated through a numerical example, showing that a high level security device can be produced using this system

Autonomous Jerk Oscillator with Cosine Hyperbolic Nonlinearity: Analysis, FPGA Implementation, and Synchronization

A two-parameter autonomous jerk oscillator with a cosine hyperbolic nonlinearity is proposed in this paper. Firstly, the stability of equilibrium points of proposed autonomous jerk oscillator is investigated by analyzing the characteristic equation and the existence of Hopf bifurcation is verified using one of the two parameters as a bifurcation parameter. By tuning its two parameters, various dynamical behaviors are found in the proposed autonomous jerk oscillator including periodic attractor, one-scroll chaotic attractor, and coexistence between chaotic and periodic attractors. The proposed autonomous jerk oscillator has period-doubling route to chaos with the variation of one of its parameters and reverse period-doubling route to chaos with the variation of its other parameter. The proposed autonomous jerk oscillator is modelled on Field Programmable Gate Array (FPGA) and the FPGA chip statistics and phase portraits are derived. The chaotic and coexistence of attractors generated in the proposed autonomous jerk oscillator are confirmed by FPGA implementation of the proposed autonomous jerk oscillator. A good qualitative agreement is illustrated between the numerical and FPGA results. Finally synchronization of unidirectional coupled identical proposed autonomous jerk oscillators is achieved using adaptive sliding mode control method

Josephson junction based on high critical-temperature superconductors: analysis, microcontroller implementation, and suppression of coexisting and chaotic attractors

A Josephson junction (JJ) based on high critical-temperature superconductors described by a linear resistive–capacitive–inductance shunted junction (LRCLSJ) model with unharmonic current-phase relation (UCPR) is theoretically and experimentally investigated in this paper. The numerical simulations indicate that JJ based on high critical-temperature superconductors exhibits excitable mode, regular spiking, periodic bursting, relaxation oscillations, chaotic attractors, and coexisting attractors. The theoretical investigations are verified experimentally through the microcontroller implementation. In addition, the coexistence between chaotic and limit cycle attractors found in JJ based on high critical-temperature superconductors is controlled to the desired trajectory using the linear augmentation control method. Finally, analytical calculations and numerical simulations are carried out to show the serviceableness of the two designed single controllers in suppressing chaos in JJ based on high critical-temperature superconductors

Dynamical analysis, FPGA implementation and its application to chaos based random number generator of a fractal Josephson junction with unharmonic current-phase relation

The dynamical characteristics and its applications to random number generator of a fractal Josephson junction with unharmonic current-phase relation (FJJUCPR) described by a linear resistive-capacitive-inductance shunted junction (LRCLSJ) model are investigated in this paper. The dependence of the equilibrium points of the system to the external current source or the unharmonic current-phase relation (UCPR) parameter is revealed and their stability are analysed. The inclusion of unharmonic current-phase relation in an ideal or a fractal Josephson junction leads to transform the spiking, bursting and relaxations oscillations to an excitable mode. While the inclusion of fractal characteristics in insulating layer of Josephson junction leads to an increase of the amplitude of the spiking, bursting and relaxations oscillations. The numerical simulations results also indicate that FJJUCPR exhibits self-excited chaotic attractors and two different shapes of hidden chaotic attractors. The FJJUCPR is implemented in field programmable gate arrays (FPGA) in order to validate the numerical simulations results. In addition, random number generator design is performed using chaotic signals of the FJJUCPR. The random number generator design results are successful in the NIST SP 800-22 test