Search Results (15)

By introducing fractional exponentiation into a three-dimensional chaotic system, a jerk system with only six terms is designed. It has the property of total amplitude control, where a single non-bifurcation parameter can directly rescale all system variables without affecting the dynamics. It also features two-dimensional offset boosting, where a single parameter can realize direct offset boosting while another provides interlocked cross-dimensional offset boosting. Furthermore, this jerk system has a parameter-dominated symmetric attractor, which means that symmetric attractors appear successively as the parameter changes from positive to negative. Circuit experiments confirm the feasibility of analog fractional exponentiation using the 444 circuit and the complete control, including amplitude control and offset boosting, of the resulting system. The proposed circuit may facilitate applications of chaotic signal generators where signal versatility is important and exemplifies the generative potential of analog fractional exponentiation. Full article

This paper designs and fabricates a small-type permanent-magnet linear motor and driver for automation applications. It covers structural design, magnetic circuit analysis, control strategies, and hardware development. Magnetic circuit analysis software JMAG is used for flux density distribution, back electromotive force (back-EMF), and electromagnetic force analysis. To address the lack of a complete closed magnetic circuit path at the ends of the linear motor, which causes magnetic field asymmetry, a phenomenon known as end effects, auxiliary core structures are proposed to compensate for the magnetic field at the ends. It successfully utilizes auxiliary cores to achieve the phase voltages of each phase, which are balanced at a phase voltage error of 0.02 V. To address the cogging force caused by variations in the magnetic reluctance of the core, this paper analyzes the relationship between electromagnetic force and mover position, conducting harmonic content analysis to obtain parameters. These parameters are applied to the designed cogging force control compensation strategy. It successfully achieves q-axis current compensation of around 1.05 A based on the mover’s position, ensuring that no jerking caused by cogging force occurs during closed-loop electromagnetic force control. The S-curve motion trajectory control is proposed to replace the traditional trapezoidal acceleration and deceleration, resulting in smoother position control of the linear motor. Simulations using JMAG-RT models in MATLAB/Simulink verified these control strategies. After verification, practical test results showed a maximum position error of approximately 5.0 μm. Practical tests show that the designed small-type permanent-magnet linear motor and its driver provide efficient, stable, and high-precision solutions for automation applications. Full article

In this paper, we propose a novel equivalent composite control architecture for electro-optical equipment. The improved tracking performance and loss of robustness caused by this structure have a clear relationship with $a_2$, the time coefficient of the compensation circuit. The compensation circuit can make the speed quality factor and the acceleration quality factor of the system infinite, and the jerk quality factor can be expanded to $1/a_2$ times the original acceleration quality factor, but it will cause a main zero point of the servo system to be far away from the virtual axis and the main poles to be close to the virtual axis. As the time coefficient of the compensation loop controller decreases, the tracking performance of the system increases, but the robustness decreases, the dynamic response deteriorates, the water bed effect becomes more obvious, and the system is more susceptible to noise and disturbances. Compared to the existing method, our method focuses on system performance and robustness. Experimental results show that our method can achieve target tracking with a peak accuracy of 64$″$ and 22$″$ (RMS), which is superior to the tracking performance without equivalent composite control. Full article

Some authors use the term cortical–subcortical myoclonus to identify a specific type of myoclonus, which differs from classical cortical myoclonus in that the abnormal neuronal activity spreads between the cortical and subcortical circuits, producing diffuse excitation. The EEG shows generalized spike-and-wave discharges that correlate with the myoclonic jerks. We report the case of a 79-year-old patient with a history of right thalamic deep hemorrhagic stroke, with favorable evolution. Fifteen years later, he was readmitted to the emergency department for episodes characterized by sudden falls without loss of consciousness. An EEG with EMG recording channel on the right deltoid muscle was performed, which documented frequent diffuse spike–wave and polyspike–wave discharges, temporally related to myoclonic jerks in the lower limbs. Brain MRI showed the persistence of a small right thalamic hemosiderin residue at the site of the previous hemorrhage. Antiseizure treatment with levetiracetam was started, with rapid clinical and electroencephalographic improvement. Our case may represent a lesion model of generalized epilepsy with myoclonic seizures. Furthermore, it highlights that lower limb myoclonus of cortical–subcortical origin may be an underestimate cause of gait disturbances and postural instability. Then, it may be reasonable to include the EEG in the diagnostic work-up of patients with recurrent falls. Full article

Mechanical jerk systems have applications in several areas, such as oscillators, microcontrollers, circuits, memristors, encryption, etc. This research manuscript reports a new 3-D chaotic jerk system with two unstable balance points. It is shown that the proposed mechanical jerk system exhibits multistability with coexisting chaotic attractors for the same set of system constants but for different initial states. A bifurcation analysis of the proposed mechanical jerk system is presented to highlight the special properties of the system with respect to the variation of system constants. A field-programmable gate array (FPGA) implementation of the proposed mechanical jerk system is given by synthesizing the discrete equations that are obtained by applying one-step numerical methods. The hardware resources are reduced by performing pipeline operations, and, finally, the paper concludes that the experimental results of the proposed mechanical jerk system using FPGA-based design show good agreement with the MATLAB simulations of the same system. Full article

This paper introduces a new chaotic jerk system with three cubic nonlinear terms. The stability properties of the three equilibrium points of the proposed jerk system are analyzed in detail. We show that the three equilibrium points of the new chaotic jerk system are unstable and deduce that the jerk system exhibits self-excited chaotic attractors. The bifurcation structures of the proposed jerk system are investigated numerically, showing period-doubling, periodic windows and coexisting bifurcations. An electronic circuit design of the proposed jerk system is designed using PSPICE. As an engineering application, a new image-encryption approach based on the new chaotic jerk system is presented in this research work. Experimental results demonstrate that the suggested encryption mechanism is effective with high plain-image sensitivity and the reliability of the proposed chaotic jerk system for various cryptographic purposes. Full article

Familial adult myoclonus Epilepsy (FAME) is a non-coding repeat expansion disorder that has been reported under different acronyms and initially linked to four main loci: FAME1 (8q23.3–q24.1), FAME 2 (2p11.1–q12.1), FAME3 (5p15.31–p15.1), and FAME4 (3q26.32–3q28). To date, it is known that the genetic mechanism underlying FAME consists of the expansion of similar non-coding pentanucleotide repeats, TTTCA and TTTTA, in different genes. FAME is characterized by cortical tremor and myoclonus usually manifesting within the second decade of life, and infrequent seizures by the third or fourth decade. Cortical tremor is the core feature of FAME and is considered part of a spectrum of cortical myoclonus. Neurophysiological investigations as jerk-locked back averaging (JLBA) and corticomuscular coherence analysis, giant somatosensory evoked potentials (SEPs), and the presence of long-latency reflex I (or C reflex) at rest support cortical tremor as the result of the sensorimotor cortex hyperexcitability. Furthermore, the application of transcranial magnetic stimulation (TMS) protocols in FAME patients has recently shown that inhibitory circuits are also altered within the primary somatosensory cortex and the concomitant involvement of subcortical networks. Moreover, neuroimaging studies and postmortem autoptic studies indicate cerebellar alterations and abnormal functional connectivity between the cerebellum and cerebrum in FAME. Accordingly, the pathophysiological mechanism underlying FAME has been hypothesized to reside in decreased sensorimotor cortical inhibition through dysfunction of the cerebellar–thalamic–cortical loop, secondary to primary cerebellar pathology. In this context, the non-coding pentameric expansions have been proposed to cause cerebellar damage through an RNA-mediated toxicity mechanism. The elucidation of the underlying pathological mechanisms of FAME paves the way to novel therapeutic possibilities, such as RNA-targeting treatments, possibly applicable to other neurodegenerative non-coding disorders. Full article

This paper is dedicated to achieving flexible automatic assembly of miniature circuit breakers (MCBs) to resolve the high rigidity issue of existing MCB assembly by proposing a flexible automatic assembly process and method with industrial robots. To optimize the working performance of the robot, a time-optimal trajectory planning method of the improved Particle Swarm Optimization (PSO) with a multi-optimization mechanism is proposed. The solution uses a fitness switch function for particle sifting to improve the stability of the acceleration and jerk of the robot motion as well as to increase the computational efficiency. The experimental results show that the proposed method achieves flexible assembly for multi-type MCB parts of varying postures. Compared with other optimization algorithms, the proposed improved PSO is significantly superior in both computational efficiency and optimization accuracy. Compared with the standard PSO, the proposed trajectory planning method shortens the assembly time by 6.9 s and raises the assembly efficiency by 16.7%. The improved PSO is implemented on the experimental assembly platform and achieves smooth and stable operations, which proves the high significance and practicality for MCB fabrication. Full article

Based on the proposed generalized memristor, a new jerk system is proposed. The complex dynamics of the system are investigated by means of bifurcation diagrams, Lyapunov exponents, and MSampEn, and rich dynamics are observed. Moreover, the circuits of the generalized memristor and the jerk system are physically implemented in the hardware level. The experimental results show that the memristor circuit can generate “8”-shaped pinched hysteresis loops, and the observed attractors match well with the numerical simulations results. In this paper, we summarize nonlinear systems with memristors in the references. It indicates that there are two symmetry methods to find a memristor model in nonlinear systems. However, some of them cannot be realized using the memristor devices, although a memristor model can be found. For example, the famous Lorenz system contains a memristor function, but it cannot be realized using the memristor device. The principles regarding whether nonlinear systems with a memristor function can be realized using a memristor device are discussed. Full article

Memristor-based systems can exhibit the phenomenon of extreme multi-stability, which results in the coexistence of infinitely many attractors. However, most of the recently published literature focuses on the extreme multi-stability related to memristor initial conditions rather than non-memristor initial conditions. In this paper, we present a new five-dimensional (5-D) two-memristor-based jerk (TMJ) system and study complex dynamical effects induced by memristor and non-memristor initial conditions therein. Using multiple numerical methods, coupling-coefficient-reliant dynamical behaviors under different memristor initial conditions are disclosed, and the dynamical effects of the memristor initial conditions under different non-memristor initial conditions are revealed. The numerical results show that the dynamical behaviors of the 5-D TMJ system are not only dependent on the coupling coefficients, but also dependent on the memristor and non-memristor initial conditions. In addition, with the analog and digital implementations of the 5-D TMJ system, PSIM circuit simulations and microcontroller-based hardware experiments validate the numerical results. Full article

This paper is about the dynamical evolution of a family of chaotic jerk systems, which have different attractors for varying values of parameter a. By using Hopf bifurcation analysis, bifurcation diagrams, Lyapunov exponents, and cross sections, both self-excited and hidden attractors are explored. The self-exited chaotic attractors are found via a supercritical Hopf bifurcation and period-doubling cascades to chaos. The hidden chaotic attractors (related to a subcritical Hopf bifurcation, and with a unique stable equilibrium) are also found via period-doubling cascades to chaos. A circuit implementation is presented for the hidden chaotic attractor. The methods used in this paper will help understand and predict the chaotic dynamics of quadratic jerk systems. Full article

A three directional (3-D) multi-scroll chaotic attractors based on the Jerk system with nonlinearity of the sine function and sign function is introduced in this paper. The scrolls in the X-direction are generated by the sine function, which is a modified sine function (MSF). In addition, the scrolls in Y and Z directions are generated by the sign function series, which are the superposition of some sign functions with different time-shift values. In the X-direction, the scroll number is adjusted by changing the comparative voltages of the MSF, and the ones in Y and Z directions are regulated by the sign function. The basic dynamics of Lyapunov exponent spectrum, phase diagrams, bifurcation diagram and equilibrium points distribution were studied. Furthermore, the circuits of the chaotic system are designed by Multisim10, and the circuit simulation results indicate the feasibility of the proposed chaotic system for generating chaotic attractors. On the basis of the circuit simulations, the hardware circuits of the system are designed for experimental verification. The experimental results match with the circuit simulation results, this powerfully proves the correctness and feasibility of the proposed system for generating 3-D grid multi-scroll chaotic attractors. Full article

This paper investigates the chaotic behavior of a modified jerk circuit with Chua’s diode. The Chua’s diode considered here is a nonlinear resistor having a symmetric piecewise linear voltage-current characteristic. To describe the system, we apply fundamental laws in electrical circuit theory to formulate a mathematical model in terms of a third-order (jerk) nonlinear differential equation, or equivalently, a system of three first-order differential equations. The analysis shows that this system has three collinear equilibrium points. The time waveform and the trajectories about each equilibrium point depend on its associated eigenvalues. We prove that all three equilibrium points are of type saddle focus, meaning that the trajectory of $\left(x\right(t),y(t\left)\right)$ diverges in a spiral form but $z\left(t\right)$ converges to the equilibrium point for any initial point $\left(x\right(0),y(0),z(0\left)\right)$. Numerical simulation illustrates that the oscillations are dense, have no period, are highly sensitive to initial conditions, and have a chaotic hidden attractor. Full article

An evergreen scientific feature is the ability for scientific works to be reproduced. Since chaotic systems are so hard to understand analytically, numerical simulations assume a key role in their investigation. Such simulations have been considered as reproducible in many works. However, few studies have focused on the effects of the finite precision of computers on the simulation reproducibility of chaotic systems; moreover, code sharing and details on how to reproduce simulation results are not present in many investigations. In this work, a case study of reproducibility is presented in the simulation of a chaotic jerk circuit, using the software LTspice. We also employ the OSF platform to share the project associated with this paper. Tests performed with LTspice XVII on four different computers show the difficulties of simulation reproducibility by this software. We compare these results with experimental data using a normalised root mean square error in order to identify the computer with the highest prediction horizon. We also calculate the entropy of the signals to check differences among computer simulations and the practical experiment. The methodology developed is efficient in identifying the computer with better performance, which allows applying it to other cases in the literature. This investigation is fully described and available on the OSF platform. Full article

A novel chaotic system for generating multi-scroll attractors based on a Jerk circuit using a special form of a sine function (SFSF) is proposed in this paper, and the SFSF is the product of a sine function and a sign function. Although there are infinite equilibrium points in this system, the scroll number of the generated chaotic attractors is certain under appropriate system parameters. The dynamical properties of the proposed chaotic system are studied through Lyapunov exponents, phase portraits, and bifurcation diagrams. It is found that the scroll number of the chaotic system in the left and right part of the x-y plane can be determined arbitrarily by adjusting the values of the parameters in the SFSF, and the size of attractors is dominated by the frequency of the SFSF. Finally, an electronic circuit of the proposed chaotic system is implemented on Pspice, and the simulation results of electronic circuit are in agreement with the numerical ones. Full article