Switching Curve Research Articles

Bifurcation detection of a neutral-type fractional-order delayed neural network via stability switching curve

Bifurcation detection of a neutral-type fractional-order delayed neural network via stability switching curve

Hopf bifurcation analysis of a two‐delayed diffusive predator–prey model with spatial memory of prey

In this paper, we consider a diffusive predator–prey model with spatial memory of prey and gestation delay of predator. For the system without delays, we study the stability of the positive equilibrium in the case of diffusion and no diffusion, respectively. For the delayed model without diffusions, the existence of Hopf bifurcation is discussed. Further, we investigate the stability switches of the model with delays and diffusions when two delays change simultaneously by calculating the stability switching curves and obtain the existence of Hopf bifurcation. We also calculate the normal form of Hopf bifurcation to determine the direction of Hopf bifurcation and the stability of bifurcation periodic solutions. Finally, numerical simulations verify the theoretical results.

Cholera disease dynamics with vaccination control using delay differential equation

The COVID-19 pandemic came with many setbacks, be it to a country’s economy or the global missions of organizations like WHO, UNICEF or GTFCC. One of the setbacks is the rise in cholera cases in developing countries due to the lack of cholera vaccination. This model suggested a solution by introducing another public intervention, such as adding Chlorine to water bodies and vaccination. A novel delay differential model of fractional order was recommended, with two different delays, one representing the latent period of the disease and the other being the delay in adding a disinfectant to the aquatic environment. This model also takes into account the population that will receive a vaccination. This study utilized sensitivity analysis of reproduction number to analytically prove the effectiveness of control measures in preventing the spread of the disease. This analysis provided the mathematical evidence for adding disinfectants in water bodies and inoculating susceptible individuals. The stability of the equilibrium points has been discussed. The existence of stability switching curves is determined. Numerical simulation showed the effect of delay, resulting in fluctuations in some compartments. It also depicted the impact of the order of derivative on the oscillations.

A Plasmonic Optoelectronic Resistive Random-Access Memory for In-Sensor Color Image Cryptography.

The optoelectronic resistive random-access memory (RRAM) with the integrated function of perception, storage and intrinsic randomness displays promising applications in the hardware level in-sensor image cryptography. In this work, 2D hexagonal boron nitride based optoelectronic RRAM is fabricated with semitransparent noble metal (Ag or Au) as top electrodes, which can simultaneous capture color image and generate physically unclonable function (PUF) key for in-sensor color image cryptography. Surface plasmons of noble metals enable the strong light absorption to realize an efficient modulation of filament growth at nanoscale. Resistive switching curves show that the optical stimuli can impede the filament aggregation and promote the filament annihilation, which originates from photothermal effects and photogenerated hot electrons in localized surface plasmon resonance of noble metals. By selecting noble metals, the optoelectronic RRAM array can respond to distinct wavelengthsand mimic the biological dichromatic cone cells to perform the color perception. Due to the intrinsic and high-quality randomness, the optoelectronic RRAM can produce a PUF key in every exposure cycle, which can be applied in the reconfigurable cryptography. The findings demonstrate an effective strategy to build optoelectronic RRAM for in-sensor color image cryptography applications.

Discrete-Event Drag Modulation Aerocapture for Mars and Titan Missions

Aerocapture is a spaceflight maneuver that uses the atmosphere of a planet or moon to slow down a spacecraft after a single atmospheric pass and capture it into an elliptical orbit around the celestial body. This paper presents a discrete-event drag modulation method for Mars and Titan aerocapture missions. A single-stage jettison is used as a control strategy to modulate the aerodynamic drag for an aerocapture scenario. Entry corridor analysis is performed under worst-case trajectory dispersions for determining the entry flight-path angle. The jettison timing of the high-drag skirt is the single free guidance parameter that adjusts the spacecraft’s trajectory during an aerocapture maneuver. A computationally simple jettison-switching guidance scheme is developed to determine when to jettison the high-drag skirt, and the result is an analytical function that represents the ballistic-coefficient switching curve. The proposed discrete-event drag-modulation strategy is extensively tested using four entry vehicles and three target orbits for Mars and Titan aerocapture scenarios. Monte Carlo simulations show that the simple switching-curve guidance provides performance metrics (apoapsis targeting errors and postexit impulsive maneuvers) that are essentially equal to the performance of more computationally burdensome guidance methods such as an onboard numerical predictor–corrector scheme.

Limit Cycles in Discontinuous Planar Piecewise Differential Systems with Multiple Nonlinear Switching Curves

Limit Cycles in Discontinuous Planar Piecewise Differential Systems with Multiple Nonlinear Switching Curves

On the Number of Limit Cycles Bifurcating from the Linear Center with a Cubic Switching Curve

On the Number of Limit Cycles Bifurcating from the Linear Center with a Cubic Switching Curve

Stability and Hopf Bifurcation Analysis of A Fractional-Order BAM Neural Network with Two Delays Under Hybrid Control

In this paper, considering that fractional-order calculus can more accurately describe memory and genetic properties, we introduce fractional integral operators into neural networks and discuss the stability and Hopf bifurcation of a fractional-order bidirectional associate memory (BAM) neural network with two delays. In addition, the hybrid controller is proposed to achieve Hopf bifurcation control of the system. By taking two time delays as the bifurcation parameters and analyzing of the corresponding characteristic equation, stability switching curves of the controllable system for two delays are obtained. The direction of the characteristic root crossing the imaginary axis in stability switching curves is determined. Sufficient criteria are sequentially given to judge the local stability and the existence of Hopf bifurcation of a fractional-order BAM neural network system. The numerical simulation results show that the hybrid controller can effectively control Hopf bifurcation of a fractional-order BAM neural network system with two delays.

The number of limit cycles of a kind of piecewise quadratic systems with switching curve y = xm

We first study the expressions for the second-order Melnikov functions for planar piecewise smooth near-Hamiltonian systems with multiple zones separated by multiple switching curves through the origin. Next, up to the second-order Melnikov functions, we consider the number of limit cycles Z(m,2) of the system x˙=y,y˙=−x with two zones separated by the curve y=xm(2≤m∈N) under the piecewise perturbations of polynomials in x and y with degree 2. It is proved that Z(2,2)=9, 13≤Z(4,2)≤19, and Z(2k,2)≥14 for k≥3 and that Z(2k+1,2)=15 for k≥2. The results are new and improve some results in the literature.

Realization of Self‐Rectifying and Self‐Powered Resistive Random‐Access Memory Memristor Using [001]‐Oriented NaNbO3 Film Deposited on Sr2Nb3O10 Nanosheet at Low Temperatures

[001]‐oriented NaNbO3 films are deposited on Sr2Nb3O10/TiN/SiO2/Si substrates at 300 °C. The Sr2Nb3O10 nanosheets are used as a template to form crystalline NaNbO3 films at low temperature. The NaNbO3 films deposited on one Sr2Nb3O10 monolayer exhibit a bipolar switching curve due to the construction and destruction of oxygen vacancy filaments. Because the Sr2Nb3O10 monolayer does not act as an insulating layer, the film does not exhibit self‐rectifying properties. Self‐rectifying properties are observed in the NaNbO3 memristor, which forms on two Sr2Nb3O10 monolayers that act as tunnel barriers in the memristor. The memristor exhibits extensive rectification and on/off ratios of 48 and 15.7, respectively. Tunneling is the current conduction mechanism of the device in the low‐resistance state, and Schottky emission and tunneling are responsible for the conduction mechanism in the high‐resistance state at low and high voltages, respectively. The piezoelectric nanogenerator produced using the [001]‐oriented NaNbO3 film generates high voltage (1.8 V) and power (3.2 μW). Furthermore, endurance of the resistive random‐access memory and nonlinear transmission characteristics of the biological synapse are accomplished in the NaNbO3 memristor powered by the NaNbO3 nanogenerator. Therefore, the [001]‐oriented crystalline NaNbO3 film formed at 300 °C may be utilized for self‐rectifying and self‐powered artificial synapses.

Revealing the nonlinear dynamics of VCSEL-based frequency combs induced by optical injection

Optical injection (OI) into VCSELs is a powerful tool to control VCSEL behavior and light emission. Previous studies by Doumbia et al. 2021 have shown that OI of a 3-line optical frequency comb (OFC) into a VCSEL allows tailoring the properties of the OFCs emitted in the VCSEL output light. Our efforts extend beyond the previous findings, as for the first time, we study the polarization-resolved nonlinear dynamics maps found in a VCSEL subject to two different types of orthogonal OI, namely continuous-wave (CW) injection and the injection of a 3-line gain-switched (GS) OFC. Our results reveal that, within a significant parameter region (encompassing frequency detuning and injected power), the VCSEL’s nonlinear behaviors induced by the OI of a GS-OFC are mainly determined by two factors: (1) the frequencies of the nonlinear dynamics of the VCSEL under CW OI, and (2) the polarization switching curves obtained under both types of OI. Therefore, (1) and (2) provide guidelines to understand the OFCs obtained at the output of the VCSEL. When injecting a 3-line OFC with 2 GHz frequency comb spacing, we demonstrate OFCs with approximately 50 GHz width at the output of the VCSEL, similar to the experimental results of Doumbia et al. 2021. We also identify the nonlinear dynamics that underpin these results.

Surface potential and mobile charge based drain current modeling of double gate junctionless accumulation mode negative capacitance field effect transistor

AbstractAn analytical drain current model for double gate junctionless accumulation mode negative capacitance field effect transistor (DG‐JAM‐NC‐FET) has been developed, combining the merits of junctionless accumulation mode and negative capacitance effect such as fabrication feasibility, low power dissipation, and reduced degradation in mobility. The novelty manifested in our work is because of the incorporation of the JAM structure in ferroelectric‐based negative capacitance FET. The benefit of JAM over existing FETs is that it combines the benefits of the junctionless transistor (JLT) and conventional FETs. It avoids excessive parasitic resistance due to stronger doping in the source and drain areas, resulting in higher conductivity and better characteristics than JLT. An analytical surface potential and threshold voltage have been developed using Poisson's equation and Landau Khalatnikov's (L‐K) equation. The drain current is then determined by integrating the mobile charge using the Pao–Sah integral. Various critical parameters such as surface potential, gain, capacitance, mobile charge density, drain current, threshold voltage, subthreshold swing, transconductance, and the switching ratio have been assessed extensively by varying ferroelectric layer and channel layer thicknesses, respectively. The ON current increases with the increase in ferroelectric thickness due to the voltage amplification given by the ferroelectric layer, and the switching curve gets steeper. The analytical modeling is done in MATLAB, and its comparison is made with the TCAD numerical simulation. The obtained analytical results and the numerical simulation results correspond well.

Stability and bifurcation analysis of Alzheimer's disease model with diffusion and three delays.

A reaction-diffusion Alzheimer's disease model with three delays, which describes the interaction of β-amyloid deposition, pathologic tau, and neurodegeneration biomarkers, is investigated. The existence of delays promotes the model to display rich dynamics. Specifically, the conditions for stability of equilibrium and periodic oscillation behaviors generated by Hopf bifurcations can be deduced when delay σ (σ=σ1+σ2) or σ3 is selected as a bifurcation parameter. In addition, when delay σ and σ3 are selected as bifurcation parameters, the stability switching curves and the stable region are obtained by using an algebraic method, and the conditions for the existence of Hopf bifurcations can also be derived. The effects of time delays, diffusion, and treatment on biomarkers are discussed via numerical simulations. Furthermore, sensitivity analysis at multiple time points is drawn, indicating that different targeted therapies should be taken at different stages of development, which has certain guiding significance for the treatment of Alzheimer's disease.

Delay Solow Model with a Normalized CES Production Function

This study analyzes the relationship between the elasticity of substitution and the economic stability/instability. To this end, we adopt a CES production function that consistently involves all its variants and introduce two delays, called a gestation delay and a depreciation delay, into the Solow model. In the case of one delay, we find that the gestation delay is harmless, the depreciation delay has a destabilizing effect, and the two delays having the equal length possesses a stronger stabilizing effect than the destabilizing effect of the depreciation delay. In the case of two different delays, we analytically construct the stability switching curve that divides the parametric region into the stability and instability regions. We also demonstrate that the location of the stability switching curve depends not only on the elasticity of substitution but the baseline values of the CES function and the parametric values of the dynamic equation.

Electron Beam‐Irradiated Au/h‐BN/Au Cross‐Point Memristors

Applying 2D materials to build memristors is a promising strategy that has attracted great interest in the semiconductor field in recent years. Although the study of memristors based on chemical vapor deposition (CVD) with lattice defects has been well established, the applications and detailed knowledge of the ones using mechanical exfoliation with good lattice structures are still scarce. Herein, the resistive switching behavior of an array of 3 μm × 3 μm cross‐point Au/25.7 nm mechanically exfoliated h‐BN/Au memristors is investigated after a controllable electron beam doping process. An electron beam irradiation strategy is first proposed to treat h‐BN memristors with intact lattice structure. Devices with moderate electron beam irradiation, which is about 1500 or 2000 mC cm−2, show good resistive switching curves. The memristor device has a repeatable resistive switching behavior, an on/off ratio of 108, a set voltage as low as 5 V, and a retention higher than 1000 s. This strategy provides an alternative method to improve the performance of memristor. Mechanical exfoliated h‐BN preserves the lattice structure, which is an immediate advantage to fabricate memristor using it compared to that fabricated by CVD.

An ITAE Optimal Sliding Mode Controller for Systems with Control Signal and Velocity Limitations

Abstract In this paper, a sliding mode controller, which can be applied for second-order systems, is designed. Robustness to external disturbances, finite regulation time and a good system’s behaviour are required for a sliding mode controller. In order to achieve the first two of these three goals, a non-linear, time-varying switching curve is introduced. The representative point (state vector) belongs to this line from the very beginning of the control process, which results in elimination of the reaching phase. The stable sliding motion along the switching curve is provided. Natural limitations such as control signal and system’s velocity constraints will be taken into account. In order to satisfy them, the sliding line parameters will be properly selected. However, a good dynamical behaviour of the system has to be provided. In order to achieve that, the integral time absolute error (ITAE) quality index will be introduced and minimised. The simulation example will verify theoretical considerations.

Optimal replenishment and transshipment management with two locations

AbstractWe study the problem of optimally managing an inventory system with backorders over a finite time horizon where the objective is minimization of expected total discounted costs. The system consists of two locations each stocking the same product. At the beginning of each time period decisions are made about replenishment at each location and about any quantity to transship between the locations before demand is observed. Leveraging the L♮‐convexity of the problem's cost function; we characterize the optimal replenishment and transshipment policy for this system. More specifically, we show the optimal policy can be described using switching curves monotone in the system state. We also discuss two extensions. For a lost‐sales model, we establish L♮‐convexity and apply it to characterize the optimal policy, simplifying the analysis found in previous work. In the other extension, we investigate the optimal policy for a partial transshipment problem where only one location orders from the external supply source and then transships to the other location.

Differential Evolution Based Numerical Variable Speed Limit Control Method with a Non-Equilibrium Traffic Model

This paper introduces a numerical variable speed limit (VSL) control method on a motorway, modeled by the system of partial differential equations (PDEs) of a non- equilibrium continuum traffic model. The method consists of a macroscopic simulation (i.e., numerical solution of the system of PDEs of the continuum model), introduction of the solution-based cost function and numerical optimization with a differential evolution algorithm (DE). Due to the numerical solution scheme, the method enables application of a wide range of continuum traffic models without prior discretization of PDEs. In this way, the method overcomes the limitations of the basic continuum models and represents a step towards more accurate traffic modelling in control strategies. In this paper, we determine optimal variable speed limits with the DE algorithm on a motorway section modeled by the modified switching curve model, which is a non-equilibrium continuum model consistent with the three-phase traffic flow theory. The effectiveness of the determined variable speed limits is validated using microsimulations of the test section, which show promising reductions of queue lengths and number of stops.

First Order Rate Law Analysis for Reset State in Vanadium Oxide Thin Film Resistive Random Access Memory Devices.

In the reset state, the decay reaction mechanism and bipolar switching properties of vanadium oxide thin film RRAM devices for LRS/HRS are investigated and discussed here. To discover the properties of I-V switching curves, the first order rate law behaviors of the reset state between the resistant variety properties and the reaction time were observed. To verify the decay reaction mechanism in the reset state, vanadium oxide thin films from RRAM devices were measured by different constant voltage sampling and exhibited the same decay reaction rate constant. Finally, the electrical conduction transfer mechanism and metallic filament forming model described by I-V switching properties of the RRAM devices were proven and investigated.

Limit cycle bifurcations of near-Hamiltonian systems with multiple switching curves and applications

<p style='text-indent:20px;'>In the present paper, we are devoted to the study of limit cycle bifurcations in piecewise smooth near-Hamiltonian systems with multiple switching curves, obtaining a formula of the first order Melnikov function in general case. As an application, we give lower bounds of the number of limit cycles for a piecewise smooth near-Hamiltonian system with a closed switching curve passing through the origin under piecewise polynomial perturbations.</p>