Switching Curve Research Articles

Bifurcation analysis in delayed Nicholson blowflies equation with delayed harvest

In this paper, we investigate a delayed Nicholson equation with delay harvesting term which was proposed in open problems and conjectures formulated by Berezansky et al. (Appl. Math. Model. 34: 1405–1417, 2010). The stability switching curves by taking two delays as parameters are obtained via the method introduced by An et al.(J. Differ. Equ. 266: 7073–7100, 2019). The existence of Hopf singularity on a two-parameter plane is determined by the varying direction of two parameters. Furthermore, the normal form near the Hopf singularity is derived via applying the center manifolds theory and normal forms method of FDEs. Finally, some numerical simulations are carried out to illustrate the theoretical conclusions.

Pulse frequency dependent synaptic characteristics in Ta/SiN/Si memristor device for neuromorphic system

We compare the filamentary resistive switching and the homogeneous resistive switching of the Ta/SiN/Si memristor device for the implementation of hardware-based neuromorphic system. The switching mode can be determined by the first switching curve. The low-resistance state (LRS) of filamentary resistive switching has stable retention properties without the resistance degradation, indicating the existence of different switching mechanisms between two. In homogeneous resistive switching mode, a more gradual increase and decrease in conductance control is possible. The multi-level states property provides better performance of pattern recognition when applied to neural network model. Finally, we demonstrate the improved frequency dependent conductance modulation in homogeneous resistive switching mode.

The optimized memristor performance by utilizing the constrained domain wall motion in Pt/Co–Tb/Ta structure

Spintronic devices can realize multilevel state storage and mimic the properties of the synapse, which enables their potential application in the field of artificial neural networks. In this paper, we demonstrate the existence of a large intermediate transition zone in current-induced magnetization switching curves of Pt/Co–Tb/Ta structures, and the number of states in the transition zone that can be manipulated by changing the Co content. The magneto-optical Kerr microscope imaging indicates that this property is related to the constrained domain wall motion in the Co–Tb films with large Co content. We also demonstrate the multilevel state storage properties of the sample by applying a sequence of current pulses. The synaptic plasticity behaviors were mimicked in these samples through regulating the value of Hall resistance by current pulses. The constrained domain wall motion supplies a simple but effective way to achieve multilevel state storage and show potential applications in neuromorphic computing.

Electrolyte Incorporation in Anodic Memristors

In the field of semiconductor electronics, the metal-oxide- semiconductor technology (CMOS) has attracted a lot of scientific attention as one of the main representatives for non-volatile memories. The development of memory systems is crucial for a fast data processing for which purpose namely microprocessors are used, following the miniaturization trends at the same time. However, the limits of CMOS technology are already exhausted in terms of power consumptions, leakage current and processing speed. Surely, novel non-volatile elements and materials are necessary to fulfill such demands and memristors are in the front as the most promising candidates.Valve metals and their oxides are frequently used as the main constitutes of metal-insulator-metal (MIM) memristive structures. Recently, Hf and Ta became the most studied valve metals playing an important role in the next-generation of thin film micro- and nano-electronic devices primarily due to applications in redox-based resistive switching memories (ReRAMs), logic circuits, sensors and artificial neural networks. The operating mechanism of memristors is based on the electric field assisted conductive filaments (CFs) formation due to the ionic drift inside the insulating oxide layer. The understanding of CFs formation is a key point to ensure excellent switching and memory characteristics of memristive devices. In accordance with the reported studies, the regulated movement of oxygen vacancies or other mobile species through the CFs can allow their pining at the constant positions and consequently high switching reproducibility of a device. Therefore, the immediate findings on the oxygen enriched media that will ensure the controlled CFs formation is of high importance. With this regard, the selection of a proper electrolyte for the fabrication of the oxide layer sandwiched between two metallic electrodes may play a significant role. It can be assumed that incorporation of electrolyte species can increase the amount of oxygen vacancies leading to a possible manipulation with their movement.Tantalum and Hf were sputtered onto Si wafers to produce thin films. Both metals were electrochemically anodized to produce oxides responsible for the memristive properties. The aim was to replace expensive fabrication methods for oxides such as sputtering or laser deposition with cost-efficient, simple and rapid anodization. The bottom electrode was either Ta or Hf thin films, Ta2O5 or HfO2 were anodic oxide layers and Pt was patterned as the top electrode, that can be seen in the inserted Figure. Two groups of these samples were anodized in the same conditions, in three electrolytes (phosphate buffer (PB), borate buffer (BB), citrate buffer (CB)) to produce three different anodic oxide layers with the thickness in the range of 20 nm. For all cases, memristive switching between high and low resistance states was demonstrated and the corresponding I-U switching curves were compared. Additionally, writing (switching) and reading tests were done for high numbers of cycles and the endurance and retention of devices were analyzed. The same tests were performed when samples were thermally treated resulting in improved or worsened switching properties, depending on the solid electrolyte placed between the metallic electrodes. Unquestionably, the use of PB, CB and BB for anodization has differently influenced the electrical properties of the memristors likely due to the trapped electrolyte species inside the oxide layer. The incorporation was confirmed by the X-ray photoelectron spectroscopy (XPS) and the presence of CFs by transmission electron microscopy (TEM). Interestingly, Ta memristors formed in PB showed the presence of Ta oxyphosphate which has induced the increase of O vacancies and thus improved switching features. However, the presence of Hf-O-P bonds found in Hf memristors that was anodized in PB did not show any improvement of electrical properties.In summary, the current study offers a reliable, controllable and cost-efficient approach for the production of ReRAMs based on Hf and Ta anodic memristors as potential candidates for the future industrial implementation. Figure 1

Identifying Key Transport Mechanisms in Organic Antiambipolar Transistors

AbstractAntiambipolar current is an enabling feature for a wide range of unconventional devices. At the same time, it still remains as a new phenomenon without sufficiently deep understanding. This article sheds light on the principles of organic antiambipolar transistors (AATs) that exploit this fundamental phenomenon, focusing on the identification of their governing charge‐transport mechanisms. Variable‐temperature current–voltage measurements are employed as a key diagnosis tool, and a series of in‐depth physical analyses are provided to directly correlate the whole AAT with its sub‐component field‐effect transistors. The gate‐selective potential transition and drift over the depleted channel are found to be responsible for the uniquely shaped AAT switching curve, thus laying a foundation for systematic device engineering.

Sliding Mode Control with Minimization of the Regulation Time in the Presence of Control Signal and Velocity Constraints

In this paper, the design of the terminal continuous-time sliding mode controller is presented. The influence of the external disturbances is considered. The robustness for the whole regulation process is obtained by adapting the time-varying sliding line. The representative point converges to the demand state in finite time due to the selected shape of the nonlinear switching curve. Absolute values of control signal, system velocity and both of these quantities are bounded from above and considered as system constraints. In order to evaluate the dynamical performance of the system, the settling time is selected as a quality index and it is minimized. The approach presented in this paper is particularly suited for systems in which one state (or a set of states) is the derivative of the other state (or a set of states). This makes it applicable to a wide range of electromechanical systems, in which the states are the position and velocity of the mechanical parts.

On the notion of vdW-force loaded hysteretic switching for precise release voltage design in all-metal electrostatic logic relay

In electrostatic switches, the inability to correlate hysteretic-switching (an electrical attribute) and adhesion force (a structural attribute) makes the predictive design difficult. The van-der-Waals interactions (FvdW) to adhesion may even be large enough to cause the release voltage (VREL) to shift past V = 0, afterward, the device never spring-back when the gate voltage is removed. The main part of this paper is devoted to addressing this issue in all-metal relay configuration. We present a physical model for shifting of VREL in its switching curve. A rule-based analytical model for VREL (precisely correlating FvdW) is first derived and found to be well fitted with the experimental data. The fabricated all-metal dielectric-less relay design mitigates the nonidealities (e.g. no work-function difference and no dielectric-charging) in FvdW calculation which is a major improvement over the past approach. Our modeling outcomes improve the understanding of how surface effects (mainly vdW force) influence the releasing sequence in M/NEMS devices that often employ contact-based switching. Temperature influence on switching characteristics is also investigated. The results demonstrate that lateral-dimensions and the temperature drive pull-out (PO) operation more dominantly than pull-in (PI).

Higher order Melnikov analysis for planar piecewise linear vector fields with nonlinear switching curve

In this paper, we are interested in providing lower estimations for the maximum number of limit cycles H(n) that planar piecewise linear differential systems with two zones separated by the curve y=xn can have, where n is a positive integer. For this, we perform a higher order Melnikov analysis for piecewise linear perturbations of the linear center. In particular, we obtain that H(2)≥4, H(3)≥8, H(n)≥7, for n≥4 even, and H(n)≥9, for n≥5 odd. This improves all the previous results for n≥2. Our analysis is mainly based on some recent results about Chebyshev systems with positive accuracy and Melnikov Theory, which will be developed at any order for a class of nonsmooth differential systems with nonlinear switching manifold.

Gradual magnetization switching via domain nucleation driven by spin–orbit torque

Gradual magnetization switching driven by spin–orbit torque (SOT) is preferred for neuromorphic computing in a spintronic manner. Here we have applied focused ion beam to selectively illuminate patterned regions in a Pt/Co/MgO strip with perpendicular magnetic anisotropy, soften the illuminated areas, and realize the gradual switching by a SOT-driven nucleation process. It is found that a large in-plane field is helpful to reduce the nucleation barrier, increase the number of nucleated domains and intermediate states during the switching progress, and finally flatten the switching curve. We proposed a phenomenological model for descripting the current dependence of magnetization and the dependence of the number of nucleation domains on the applied current and magnetic field. This study may promote the birth of SOT devices applicable in neuromorphic computing applications.

Optimized state-dependent switching law design for a class of switched nonlinear systems with two unstable subsystems

This paper proposes a new method for designing a state-dependent switching law to stabilize a class of switched nonlinear system with two unstable subsystems. The main idea is to convert each subsystem to a second-order mechanical system by introducing a reversible transformation, thus the summation of its kinetic and potential energies is calculated as an energy function. Then, by defining a performance index with energy function and using the variational principle, two optimal switching curves are derived from the Euler equation. By adopting a switching law designed by such switching curves, the state of the switched system can approach to the origin at the fastest speed in a sense. In addition, for the case of switched systems with linear vibration subsystems, a critical stability condition related to the stiffness and negative damping coefficients of the subsystems is obtained to make the switched system periodic. Finally, simulation results show that the proposed method can effectively solve the stability problem of switched systems, in which each subsystem does not have any stability factors.

Optimal Production Control of Remanufacturing Systems Based on a Queueing Model With Returns

This paper analyzes an optimal dynamic production control problem of a remanufacturing system in stochastic environment. The system consists of one inventory for serviceable items and one virtual inventory for the items used by customers which will be either remanufactured to be serviceable items or discarded. Demands will be lost if there is no serviceable items available. At any decision epoch, the decision maker has to decide whether to produce items or not by raw materials, so as to minimize the long run average cost. The optimization problem is constructed as a Markov decision process (MDP). We show that the optimal policy has a multi-threshold structure (switching curve) and it is monotonic in system parameters. Furthermore, based on the structure of the optimal policy, we construct a performance evaluation model for computing efficiently the optimal thresholds. The expression of the average cost is given by a quasi-birth-death (QBD) process. Finally, we provide some numerical results to show the effectiveness of our approach and the impact of different parameters on the optimal policy and average cost.

Mathematical modeling of intervention and low medical resource availability with delays: Applications to COVID-19 outbreaks in Spain and Italy.

Infectious diseases have been one of the major causes of human mortality, and mathematical models have been playing significant roles in understanding the spread mechanism and controlling contagious diseases. In this paper, we propose a delayed SEIR epidemic model with intervention strategies and recovery under the low availability of resources. Non-delayed and delayed models both possess two equilibria: the disease-free equilibrium and the endemic equilibrium. When the basic reproduction number $ R_0 = 1 $, the non-delayed system undergoes a transcritical bifurcation. For the delayed system, we incorporate two important time delays: $ \tau_1 $ represents the latent period of the intervention strategies, and $ \tau_2 $ represents the period for curing the infected individuals. Time delays change the system dynamics via Hopf-bifurcation and oscillations. The direction and stability of delay induced Hopf-bifurcation are established using normal form theory and center manifold theorem. Furthermore, we rigorously prove that local Hopf bifurcation implies global Hopf bifurcation. Stability switching curves and crossing directions are analyzed on the two delay parameter plane, which allows both delays varying simultaneously. Numerical results demonstrate that by increasing the intervention strength, the infection level decays; by increasing the limitation of treatment, the infection level increases. Our quantitative observations can be useful for exploring the relative importance of intervention and medical resources. As a timing application, we parameterize the model for COVID-19 in Spain and Italy. With strict intervention policies, the infection numbers would have been greatly reduced in the early phase of COVID-19 in Spain and Italy. We also show that reducing the time delays in intervention and recovery would have decreased the total number of cases in the early phase of COVID-19 in Spain and Italy. Our work highlights the necessity to consider the time delays in intervention and recovery in an epidemic model.

Оптимальне демпфування відхилень кутових швидкостей осесиметричного космічного літального апарата

This paper considers the problem of optimal fuel consumption damping of sudden deviations of angular velocities of an axisymmetric spacecraft with a constant speed of rotation around the main axis of symmetry. This assumption has some practical significance and may be due to the creation of artificial gravity on the spacecraft. The idea of artificial gravity due to the rotation of an axisymmetric cylindrical spacecraft is based on the principle of equivalence of the force of gravity and the force of inertia. The urgency of the fuel consumption optimization problem is due to the presence of its limited stock onboard the spacecraft. The optimization problem is solved based on the maximum principle and the phase plane method. The authors of the article determine the structure of optimal fuel consumption processes with three levels of control, and the number of their switches depends on the initial conditions. Synthesized on the phase plane, the optimal switching curves divide the phase plane into eight curvilinear quadrants, which uniquely determine the values of the optimal control effects by the current values of the deviations of the angular velocities of the spacecraft. The problem of the possible presence of a delay in the control loop is proposed to be solved based on the Bess compensation method. To do this, the corresponding optimal curves of switching and disabling the controls are built as geometric locations of points remoted for the time of delay from the found curves of switching and the beginning of coordinates accordingly. It allows us to avoid the emergence of steady self-oscillations in a control contour and to provide a condition of keeping the spacecraft in a given final state after the completion of the stabilization process. Depending on the technical equipment of the spacecraft, two variants of the optimal damping algorithm are offered, namely: an autonomous device in the onboard control system of the spacecraft in the absence of a sufficiently powerful onboard computer, or the optimal damping algorithm, implemented entirely in the onboard computer of the spacecraft in case of its sufficient power.

Double Hopf bifurcation of a diffusive predator–prey system with strong Allee effect and two delays

In this paper, we consider a diffusive predator–prey system with strong Allee effect and two delays. First, we explore the stability region of the positive constant steady state by calculating the stability switching curves. Then we derive the Hopf and double Hopf bifurcation theorem via the crossing directions of the stability switching curves. Moreover, we calculate the normal forms near the double Hopf singularities by taking two delays as parameters. We carry out some numerical simulations for illustrating the theoretical results. Both theoretical analysis and numerical simulation show that the system near double Hopf singularity has rich dynamics, including stable spatially homogeneous and inhomogeneous periodic solutions. Finally, we evaluate the influence of two parameters on the existence of double Hopf bifurcation.

Stability switching and its directions in cournot duopoly game with three delays

<p style='text-indent:20px;'>A three-delay duopoly is considered where the firms have identical implementation delays with different information delays. The equilibrium is locally asymptotically stable without delays however this stability is lost with increasing values of the delays. The stability properties of the equilibrium depend on the common implementation delay of the firms and on the sum of the two information delays. The stability switching curves are first analytically characterized and illustrated, and then the direction of the stability switching is determined at each point of the curves. The possibility of multiple pure imaginary eigenvalues is also discussed when the directions of the stability switches cannot be determined. Simulation examples illustrate the theoretical results.</p>

Delay Cournot Duopoly Game with Gradient Adjustment: Berezowski Transition from a Discrete Model to a Continuous Model

This paper investigates the asymptotical behavior of the equilibrium of linear classical duopolies by reconsidering the two-delay model with two different positive delays. In a two-dimensional analysis, the stability switching curves were first analytically determined. Numerical studies verified and illustrated the theoretical results. In the sensitivity analysis it was demonstrated that the inertia coefficient has a twofold effect: enlarges the stability region as well as simplifies the complicated dynamics with period-halving cascade. In contrary, the adjustment speed contracts the stability region and complicates simple dynamics with period-doubling bifurcation. In addition, for various values of τ1 and τ2, a wide variety of dynamics appears ranging from simple cycle via a Hopf bifurcation to chaotic oscillations.

Time delays and chaos in two competing species revisited

This paper reexamines the Lotka-Volterra competition model with two delays. The steady state is shown to be locally asymptotically stable without delay. If the two delays are identical, then the model becomes a one-delay system. The critical value of the delay is determined when stability might be lost. If the delays are different, then the stability switching curves are analytically defined and numerically verified. It is demonstrated that the unstable two-delay system may exhibit periodic behavior, multistability, quasi period-doubling cascade and even complicated dynamics depending on model parameters.

Limit cycle bifurcations of piecewise smooth near-Hamiltonian systems with a switching curve

<p style='text-indent:20px;'>This paper deals with the number of limit cycles for planar piecewise smooth near-Hamiltonian or near-integrable systems with a switching curve. The main task is to establish a so-called first order Melnikov function which plays a crucial role in the study of the number of limit cycles bifurcated from a periodic annulus. We use the function to study Hopf bifurcation when the periodic annulus has an elementary center as its boundary. As applications, using the first order Melnikov function, we consider the number of limit cycles bifurcated from the periodic annulus of a linear center under piecewise linear polynomial perturbations with three kinds of quadratic switching curves. And we obtain three limit cycles for each case.

A MEAN FIELD GAME ANALYSIS OF SIR DYNAMICS WITH VACCINATION

We analyze a mean field game model of SIR dynamics (Susceptible, Infected, and Recovered) where players choose when to vaccinate. We show that this game admits a unique mean field equilibrium (MFE) that consists in vaccinating at a maximal rate until a given time and then not vaccinating. The vaccination strategy that minimizes the total cost has the same structure as the MFE. We prove that the vaccination period of the MFE is always smaller than the one minimizing the total cost. This implies that, to encourage optimal vaccination behavior, vaccination should always be subsidized. Finally, we provide numerical experiments to study the convergence of the equilibrium when the system is composed by a finite number of agents ($N$) to the MFE. These experiments show that the convergence rate of the cost is$1/N$and the convergence of the switching curve is monotone.

Delay Stability of n-Firm Cournot Oligopolies

The dynamic behavior of n-firm oligopolies is examined without product differentiation and with linear price and cost functions. Continuous time scales are assumed with best response dynamics, in which case the equilibrium is asymptotically stable without delays. The firms are assumed to face both implementation and information delays. If the delays are equal, then the model is a single delay case, and the equilibrium is oscillatory stable if the delay is small, at the threshold stability is lost by Hopf bifurcation with cyclic behavior, and for larger delays, the trajectories show expanding cycles. In the case of the non-equal delays, the stability switching curves are constructed and the directions of stability switches are determined. In the case of growth rate dynamics, the local behavior of the trajectories is similar to that of the best response dynamics. Simulation studies verify and illustrate the theoretical findings.