Narrow Results

This paper is associated with the manufacture of 60W Transverse Flux Linear Motor (TFLM), and the thrust force and the maximum displacement of TFLM is compared with Longitudinal Flux Linear Motor (LFLM). Thus, the force which follows in location of the electric motor is simulated with ANSYS, and the thrust force of the linear actuator with applied current is tested. And the experiment results by several cases of alternating current is reported.

The effects of noise correlation and time delay on the transient properties of a cancer growth system are studied in terms of the mean first-passage time (MFPT), which provides a measure of the mean extinction time of the tumor cell population. The results indicate that the additive and multiplicative noises can induce the noise-enhanced stability (NES) effect. The increasing of the delay time weakens the NES effect in the presence of two noise sources and induces a shift of the maximum of the MFPT towards smaller values of the noise intensities. The increasing of cross-correlation strength between noises can only restrain the NES effect induced by the multiplicative noise and can induce a shift of the peak of the MFPT towards larger values of the noise intensities.

The phenomenon of stochastic resonance (SR) in a time-delayed bistable system with colored coupling between multiplicative and additive noise terms is investigated. The SR can be induced by the multiplicative noise, the time delay and the coupling strength between noise terms. Meanwhile, the SR is affected by the initial condition of the system.

The steady properties of a stochastic single genetic regulation system with the different time delays, which appear in the deterministic and fluctuating forces, are investigated based on the small delay time approximation method. Using the approximation probability density approach, the delayed Fokker–Planck equation is obtained. The effects of two different time delays on the stationary probability distribution and the mean value are discussed. It is found that with the time delay τ₁ in the deterministic force increasing, the TF-A monomer concentration shifts from "off" state to "on" state. However, with the time delay τ₂ in the fluctuating force increasing, the TF-A monomer concentration shifts from "on" state to "off" state. In the switch process, two kinds of time delays play an opposite role. The theoretical predictions are found to be in good agreement with numerical results.

The effects of time delay on the vibrational resonance (VR) in a discrete neuron system with a low-frequency signal and a high-frequency signal are investigated by numerical simulations. The results show that there exists a delay time that optimizes the phase synchronization between the low-frequency input signal and the output signal. VR is induced by the time delay. Furthermore, the time delay can improve the response to a low-frequency input signal. Therefore, the time delay plays a constructive role in the transmission of a low-frequency signal by inducing and enhancing VR.

The electric activity of neuron and collective behaviors of neurons can be modulated by autapse, which can be described by self-feedback current in close loop with time delay being considered. Distribution of electric autapses in a local area can introduce heterogeneity in the network and thus traveling wave emits from this area. In this paper, diversity in time delay of electric autapse is considered and collision between emitting waves from different local areas driven by electric autapses under different time delays is observed. In the numerical studies, neurons in the square area with 15×15 (and/or 20×20) nodes are connected electric autapses with different time delays and target-like waves are induced and converted into, spiral waves after continuous collision between wave fronts. It is found that a group of spiral waves can emerge in the network, or coexist with target waves under appropriate coupling intensity due to time delay diversity in autapse and these waves can regulate the collective behaviors of neurons as continuous pacemakers.

With the fully classical ensemble model, we investigate the correlated electron dynamics of nonsequential double ionization (NSDI) by few-cycle laser pulses at 3T (T is the laser cycle) and compared it with the 6T case. For the 6T laser pulse, the momentum distribution of correlated electron in the direction parallel to the laser polarization exhibits a V-like structure which has been observed in the experiment. [Camus et al., Phys. Rev. Lett.108, 073003 (2012)]. However, for the 3T laser pulse, the momentum distribution shows a surprising arc-like structure. Meanwhile, the correlated electron momentum spectrum in the direction perpendicular to the laser polarization shows a more stronger anticorrelated behavior for the 3T laser pulse than that of the 6T laser pulse. By analyzing all the classical trajectories of NSDI, for the 3T laser pulse, the contribution to NSDI only comes from the first return and the latter returns are completely supressed, which is different from the case of the 6T laser pulse where not only the first return but also the latter returns contribute to the NSDI events. Moreover, the recolliding energies are often higher for the 3T laser pulse than that of the 6T laser pulse due to a more rapid turn on of laser field for the 3T laser pulse which plays a key role for the arc-like structure. The more energetic recollisions that occur in the 3T laser pulse lead to greater anticorrelation in the transverse momenta than is observed in the 6T laser pulse with less energetic recollisions.

In this paper, the gene transcriptional dynamics driven by correlated noises are investigated, where the time delay for the synthesis of transcriptional factor is introduced. The effects of the noise correlation strength and time delay on the stationary probability distribution (SPD), the mean first passage time and the stochastic resonance (SR) are analyzed in detail based on the delay Fokker–Planck equation. It is found that both the time delay and noise correlation strength play important roles in the bistable transcriptional system. The effect of the correlation strength reduces but the time delay enhances the mean first passage time (MFPT). Finally, the SR for this gene transcriptional system is found to be enhanced by the time delay.

We investigate the synchronization of time-delayed complex dynamical networks with periodic on-off coupling. We derive sufficient conditions for the complete and generalized outer synchronization. Both our analytical and numerical results show that two time-delayed networks can achieve outer synchronization even if the couplings between the two networks switch off periodically. This synchronization behavior is largely dependent of the coupling strength, the on-off period, the on-off rate and the time delay. In particular, we find that the synchronization time nonmonotonically increases as the time delay increases when the time delay step is not equal to an integer multiple of the on-off period.

We investigate the oscillating dynamics in a ring of network of nonlocally delay-coupled fractional-order Stuart-Landau oscillators. It is concluded that with the increasing of coupling range, the structures of death islands go from richness to simplistic, nevertheless, the area of amplitude death (AD) state is expanded along coupling delay and coupling strength directions. The increased coupling range can prompt the coupled systems with low frequency to occur AD. When system size varies, the area of death islands changes periodically, and the linear function relationship between periodic length and coupling range can be deduced. Thus, one can modulate the oscillating dynamics by adjusting the relationship between coupling range and system size. Furthermore, the results of numerical simulations are consistent with theoretical analysis.

This paper mainly concerns with the finite-time synchronization of delayed fractional-order quaternion-valued memristor-based neural networks (FQVMNNs). First, the FQVMNNs are studied by separating the system into four real-valued parts owing to the noncommutativity of quaternion multiplication. Then, two state feedback control schemes, which include linear part and discontinuous part, are designed to guarantee that the synchronization of the studied networks can be achieved in finite time. Meanwhile, in terms of the stability theorem of delayed fractional-order systems, Razumikhin technique and comparison principle, some novel criteria are derived to confirm the synchronization of the studied models. Furthermore, two methods are used to obtain the estimation bounds of settling time. Finally, the feasiblity of the synchronization methods in quaternion domain is validated by the numerical examples.

Inhibitory effect often suppresses electronic activities of the nervous system. In this paper, the inhibitory autapse is identified to enhance the degree of coherence resonance (CR) induced by noise in the Hodgkin–Huxley (HH) model with Hopf bifurcation from resting state to spiking with nearly fixed period $T_2$. Without noise, the inhibitory autapse can induce a post inhibitory rebound (PIR) spike from the resting state at time delay approximating $T_1$ and can inhibit a spike of spiking at time delay approximating $T_2$. In the presence of noise, CR characterized by maximal value of power spectrum of spike trains appears in a wide range of both time delay and conductance of autapse. With increasing autaptic conductance, CR degree becomes stronger for time delay approximating $T_1$ plus integer (from 0) multiples of $T_2$, because the inhibitory autaptic current pulses can induce more PIR spikes. The decrease of CR degree at time delay approximating integer (from 1) multiples of $T_2$ can be explained by the inhibition effect. The promotion of coherence resonance degree and the underlying PIR mechanism induced by inhibitory self-feedback extends the paradoxical phenomenon of inhibitory autapse to stochastic system and presents potential measures to modulate CR degree and information processing.

Since the concept of memristor was proposed, the memristor, as the fourth-generation electronic component, has attracted great attention from researchers. Memristors can be used not only for nonvolatile memory but also to mimic the behavior of nervous system. The inherent nonlinearity of memristor makes it valuable in nonlinear circuits. Since it is still difficult to realize the commercial application of memristors at present, designing suitable memristor models can play a guiding role in practical application. This work proposes a novel memristor model with a time-delay state variable. The proposed memristor cannot only generate pinched hysteresis loop under periodic signal excitation, but also can generate chaotic current or even hyperchaotic current under DC voltage. The nonlinear dynamics of the proposed time-delay memristor are studied by phase portraits, bifurcation diagram and Lyapunov exponents. Furthermore, the proposed memristor is used in the HR neuron model to study neuronal electrical activities with electromagnetic induction. Multiple firing patterns of the memristive neuron can be generated such as periodic, bursting and chaotic. Finally, the memristor emulator circuit and the HR neuron model circuit are designed and simulated by Pspice.

This paper focuses on the issue of fuzzy resilient control for synchronizing chaotic systems with time-variant delay and external disturbance. The goal is to design a fuzzy resilient controller with additive gain perturbations to guarantee that not only the drive and response systems are asymptotically synchronized in the absence of external disturbance, but also the synchronization error system has a prescribed disturbance attenuation index under the zero initial condition. By utilizing an appropriate Lyapunov–Krasovskii functional, the Bessel–Legendre inequality, and the reciprocally convex combination technique, a criterion on the stability and ${{\mathscr{H}}}_{\infty }$ performance of the synchronization error system is derived. Then, by means of some decoupling methods, a design scheme of the fuzzy resilient controller is developed. Finally, one numerical example is provided to examine the effectiveness of the fuzzy resilient controller design scheme.

In this paper, the dynamical behavior of the FitzHugh–Nagumo (FHN) neural system with time delay driven by Lévy noise is studied from two aspects: the mean first-passage time (MFPT) and the probability density function (PDF) of the first-passage time (FPT). Using the Janicki–Weron algorithm to generate the Lévy noise, and through the order-4 Runge–Kutta algorithm to simulate the FHN system response, the time that the system needs from one stable state to the other one is tracked in the process. Using the MATLAB software to simulate the process above 20,000 times and recording the PFTs, the PDF of the FPT and the MFPT is obtained. Finally, the effects of the Lévy noise and time-delay on the FPT are discussed. It is found that the increase of both time-delay feedback intensity and Lévy noise intensity can promote the transition of the particle from the resting state to the excited state. However, the two parameters produce the opposite effects in the other direction.

Neurons contain a large number of ions inside and outside the cell, and the transmembrane currents formed by the movement of these ions cause membrane potential fluctuations and induce electromagnetism inside and outside the cell. In addition, any change in external electromagnetic fields can cause changes in the membrane potential of the neurons. Therefore, based on the three-dimensional Hindmarsh — Rose (HR) neuron model, a five-dimensional neuron model with time delay is developed in this paper by introducing flux and electric field variables and considering the resulting time delay. First, the Hopf bifurcation theory is used to demonstrate the local stability of the system at the equilibrium point at different time delays. Then, the stability of the Hopf bifurcation and its direction are proved by using the central flow shape theorem. Finally, the existence of the Hopf bifurcation is proved using the phase diagram and the bifurcation diagram, and the effects of several important parameters on the model are investigated by numerical simulations using time series plots, ISI bifurcation plots and two-parameter bifurcation plots. The model is found to be accompanied by chaotic and chaos-free plus-periodic bifurcation structures, mixed-mode discharges and other phenomena. Also, its discharge pattern can be controlled after adding time delay. The results of this paper provide help to the pathogenic mechanism and control of neurological diseases.

Neurons are connected through synapses, but it is not reasonable to equate the connection mode of synapses to an edge in the network due to synaptic plasticity whereas the magnetic field coupling can be considered to handle it. Therefore, in this paper, the interaction between HR neurons is realized by magnetic field coupling based on induction coil, and time delay is introduced to represent the lag in information transfer. First, the coexisting firing activities and synchronization behaviors in dual neuronal networks are numerically calculated, respectively, depending on the external stimulation current, coupling strength, time delays, and initial conditions. When the time delays are given, it is interesting to note that the infinite number of firing modes including chaotic firing, periodical firing, and quiescent state is induced by initial conditions. Due to the initial values, the types of synchronization consisting of complete synchronization, delayed synchronization, and asynchronization are then revealed under the framework of extreme multistability. In particular, the state of complete synchronization exhibits only quiescent state and period-1 firing when the time delay is not equal to 0. Furthermore, the linear augmentation method is conceived to control extreme multistability. It can be found that the attractors with different positions and topological structures can be controlled to the point attractors with the same shape but with different positions when the coupling strength of linear system and nonlinear system is increased. That is, the heterogeneous multistability can be successfully controlled to the homogeneous multistability, and the coupled neurons can also be achieved synchronization after control. These conclusions in this paper could be helpful in providing new insights for studying neurodynamics and applying neural circuits.

In this paper, an identification method is proposed for linear continuous time delay processes with unknown non-zero initial condition and disturbance from pulse tests. Multiple integral is used and integral intervals are specifically chosen to enable easy identification of the system parameters in one step. The effectiveness of the identification method is demonstrated through simulations.

We study the effects of time delay on stochastic resonance (SR) in the tumor cell growth model driven by two coupled noises and a weak external periodic signal. Under the condition of small delay time, we obtained the signal-to-noise ratio (SNR) R_SNR from the quasi-steady-state probability distribution function through the adiabatic elimination method and the SR theory about a two-state transition. By the numerical computations, we discussed the effects of the delay time τ on the SNR as a function of the multiplicative noise intensity D, the additive noise intensity α and the cross-correlated strength λ respectively. The appearance of a peak in these curves represents the SR phenomenon. It is found that with the increase of τ, the SR is suppressed in the D–R_SNR plot and weakened in the α–R_SNR plot. However, the SR is strengthened with the increase of τ in the λ–R_SNR plot.

We study dynamical properties of an anti-tumor cell growth system in the presence of time delay and correlations between multiplicative and additive white noise. Using the small time delay approximation, the Novikov theorem and Fox approach, the stationary probability distribution (SPD) is obtained. Based on the SPD, the expressions of the normalized correlation function C(s) and the associated relaxation time T_c are derived by means of Stratonovich decoupling ansatz. Based on numerical computations, we find the following: (i) The SPD exhibits one-peak → two-peaks → one-peak phase transitions as the correlation intensity λ varies. (ii) The relaxation time T_c exhibits a one-peak structure for negatively correlated noise (λ<0), however for positively correlated noise (λ>0), the relaxation time T_c decreases monotonously. (iii) The effects of the delay time τ on T_c and C(s) are entirely the same for λ<0 and for λ>0, i.e. τ enhances the fluctuation decay of the population of tumor cells.