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The dynamics of neural networks has been widely concerned by scholars. However, most of the previous results on dynamical bifurcations are limited to few nodes coupling neural networks which modeled by differential equations with integer-order derivative, and few efforts have been contributed to studying the bifurcation behaviors of large-scale fractional-order neural networks. Furthermore, the structural characteristics of networks are also of great research value. Among them, the ring structure is a common phenomenon in neural networks. Although there are few papers on the bifurcation analysis of ring-structured neural networks recently, they consider only the case of a single ring. In this article, the dynamical analysis and design for a class of large-scale-delayed fractional-order neural networks with multiple rings and hub structure are investigated. First, the time delay is considered to be the bifurcation parameter and the formula of Coates’ flow graph is adopted to obtain the characteristic equation of large-scale networks. Second, by analyzing the complex radial and circular connections of neurons, the delay-induced Hopf bifurcation sufficient conditions for the neural network are established. Finally, the theoretical results are substantiated by a number of numerical simulation experiments and the relationships between the onset of bifurcation and the fractional order, the number of neurons, and the number of rings are revealed. [ABSTRACT FROM AUTHOR]

The increase in queueing delays in the Internet motivates the study of transmission control protocol (TCP) and queue management policies. This paper studies Compound TCP with a Proportional–Integral (PI) policy for queue management at the Internet routers. A nonlinear fluid model for the Compound TCP-PI system is considered. For this model, a sufficient condition for local stability, which yields some design guidelines, is derived. Fragility analysis of this model highlights that even marginal variations in the PI parameters may induce instability. Next, a regime where the integral component, of the PI policy, operates over a small time-scale is considered. For a fluid model befitting this regime, the necessary and sufficient condition for local stability is derived. It is explicitly shown that, when this condition is violated, the system undergoes a Hopf bifurcation, which would lead to limit cycles. Furthermore, a detailed local bifurcation analysis is conducted to characterize the type of the Hopf bifurcation and determine the orbital stability of the limit cycles. Packet-level simulations corroborate the analytical insight. The analysis and simulations demonstrate some drawbacks of the PI policy. Following this, a simple threshold-based queue policy, which has desirable stability properties, is proposed for queue management at routers. Furthermore, a simulation-based performance evaluation reveals that this policy outperforms PI. Through a combination of theory and simulations, it is shown that the threshold-based policy can ensure system stability, while ensuring reduced queueing delays. [ABSTRACT FROM AUTHOR]

This is the second part of a two-part paper presenting a dynamic state feedback control law that guarantees the elimination of Hopf bifurcations before the occurrence of a saddle-node bifurcation. In Part I, the mathematical representation of the system's dynamics, Hopf, and Saddle-Node bifurcation theorems, and the state feedback controller design were presented. In this part, to illustrate the system analysis methodology, control design, and to carry out performance evaluation of the controller, both single-machine and multimachine power systems are analyzed. To highlight the effect of saturation phenomena, bifurcation analyses are performed before and after detailed modeling of synchronous generator saturation, for the single-machine power system case. The multimachine case is used to illustrate the scalability and applicability of the method to generic power networks. [ABSTRACT FROM AUTHOR]

This two-part paper introduces a dynamic state feedback control law that guarantees the elimination of Hopf bifurcations (HB) before reaching the saddle-node bifurcations (SNB). Part I is devoted to the mathematical representation of the detailed system dynamics, investigation of HB and SNB theorems, and state feedback controller design. For purposes of dynamical analysis, the stable equilibria of the system is obtained. Then the control system is designed with the objective of preventing the voltage collapse before the SNB, such that the structural stability of the system is preserved in the stationary branch of the solutions. The controller aims to relocate Hopf bifurcations to the stationary branch of solutions located after SNB, eliminating the HB from normal operating region of the system. In order to evaluate the performance of the proposed controller, bifurcation analysis has been performed in Part II using single-machine and multi-machine test systems. [ABSTRACT FROM AUTHOR]

Complete stability analyses, including voltage, small perturbation and transient stability studies, and the associated models and controls of a series vectorial compensator (SVeC) are presented in this paper. It is also shown through detailed simulations that the SVeC is a competitive device against series power-flow controllers and it might be a better option for similar purposes where space and costs are at premium. Hence, a full comparative evaluation of this controller with respect to controllers used mainly for oscillation control in transmission corridors, namely, thyristor-controlled series capacitors (TCSC) and series static synchronous compensators (SSSC), is also presented for the first time. The IEEE 14-bus benchmark system and a 190-bus, 46-machine model of the Mexican grid are used for illustrative and comparison purposes. The results obtained show that the SVeC has better oscillation damping characteristics than the TCSC and SSSC, hence making these types of controllers a competitive alternative against existing series flexible ac transmission system (FACTS) controllers for dynamic series compensation of transmission lines. [ABSTRACT FROM AUTHOR]

Hysteresis in power amplifiers (PAs) is investigated in detail with the aid of an efficient analysis method, compatible with commercial harmonic balance. Suppressing the input source and using, instead, an outer-tier auxiliary generator, together with the Norton equivalent of the input network, analysis difficulties associated with turning points are avoided. The turning-point locus in the plane defined by any two relevant analysis parameters is obtained in a straightforward manner using a geometrical condition. The hysteresis phenomenon is demonstrated to be due to a nonlinear resonance of the device input capacitance under near optimum matching conditions. When increasing the drain bias voltage, some points of the locus degenerate into a large-signal oscillation that cannot be detected with a stability analysis of the dc solution. In driven conditions, the oscillation will be extinguished either through synchronization or inverse Hopf bifurcations in the upper section of the multivalued curves. For an efficient stability analysis, the outer-tier method will be applied in combination with pole-zero identification and Hopf-bifurcation detection. Departing from the detected oscillation, a slight variation of the input network will be carried out so as to obtain a high-efficiency oscillator able to start up from the noise level. All the tests have been carried out in a Class-E GaN PA with measured 86.8% power-added efficiency and 12.4-W output power at 0.9 GHz. [ABSTRACT FROM AUTHOR]

Stochastic optimal power flow can provide the system operator with adequate strategies for controlling the power flow to maintain secure operation under stochastic parameter variations. One limitation of stochastic optimal power flow has been that only limits on line flows have been used as stability constraints. In many systems voltage stability and small-signal stability also play an important role in constraining the operation. [ABSTRACT FROM PUBLISHER]

An in-depth investigation of oscillation modes in ring oscillators is presented. The small-signal stability is initially considered, demonstrating that the poles associated with the dc regime are uniformly distributed on a circle on the complex plane, with increasing density for a higher number of stages. The existence of multiple pairs of poles on the right-hand side of the complex plane gives rise to different oscillation modes, related here to the eigenvectors of the circulant active-device immitance matrix. This paper shows that the stability properties of detected modes depend on both the order of appearance from dc regime, in a sequence of Hopf bifurcations, and the bifurcations undergone by each steady-state mode until reaching the final operation point, when changing a bias voltage, for instance. Thus, the stability analysis must combine a bifurcation analysis from dc regime and a bifurcation analysis of each individual oscillation mode in large-signal regime. The large-signal stability analysis presented shows the possible stabilization mechanisms, which lead to the common physical observation of some of these modes. The stabilization of the desired mode, using concepts from bifurcation theory, is also presented. All techniques have been successfully applied to a ring oscillator at 12.6 GHz. [ABSTRACT FROM AUTHOR]

A new methodology for the detection of Hopf, flip, and turning-point bifurcations in nonlinear circuits analyzed with harmonic balance (HB) is presented. It enables a systematic determination of bifurcation loci in terms of relevant parameters, such as input power, input frequency, and bias voltages, for instance. It does not rely on the use of continuation techniques and is able to globally provide the entire loci, often containing multivalued sections and/or disconnected curves, in a single simulation. The calculation of Hopf and flip bifurcations is based on the extraction of a small-signal admittance/impedance function from HB and the calculation of its zeros through a geometrical procedure. The method is ideally suited for the investigation of the global stability properties of power amplifiers and other nonlinear circuits. The turning-point locus, associated with either jump phenomena or synchronization, is obtained by taking into account the annihilation/generation of steady-state solutions that is inherent to this type of bifurcation. A technique is also presented for the exhaustive calculation of oscillation modes in multidevice oscillators and oscillators loaded with multiresonance networks. The new methodologies are illustrated through their application to a power amplifier and a multimode oscillator. [ABSTRACT FROM AUTHOR]

We study Compound TCP (C-TCP), the default TCP in the Windows operating system, with Random Exponential Marking (REM) and the widely used Drop-Tail queue policy. The performance metrics we consider are stability of the queue size, queuing delay, link utilization, and packet loss. We analyze the following models: 1) a nonlinear model for C-TCP with Drop-Tail and small buffers; 2) a stochastic variant of REM along with C-TCP; and 3) the original REM proposal as a continuous-time nonlinear model with delayed feedback. We derive conditions to ensure local stability and show that variations in system parameters can induce a Hopf bifurcation, which would lead to the emergence of limit cycles. With Drop-Tail and small buffers, the Compound parameters and the buffer size both play a key role in ensuring stability. In the stochastic variant of REM, larger thresholds for marking/dropping packets can destabilize the system. With the original REM proposal, using Poincaré normal forms and the center manifold analysis, we also characterize the type of the Hopf bifurcation. This enables us to analytically verify the stability of the bifurcating limit cycles. Packet-level simulations corroborate some of the analysis. Some design guidelines to ensure stability and low latency are outlined. [ABSTRACT FROM PUBLISHER]

Dynamic response of loads has a significant effect on system stability and directly determines the stability margin of the operating point. Inherent uncertainty and natural variability of load models make the stability assessment especially difficult and may compromise the security of the system. We propose a novel mathematical “robust stability” criterion for the assessment of small-signal stability of operating points. Whenever the criterion is satisfied for a given operating point, it provides mathematical guarantees that the operating point will be stable with respect to small disturbances for any dynamic response of the loads. The criterion can be naturally used for identification of operating regions secure from the occurrence of Hopf bifurcation. Several possible applications of the criterion are discussed, most importantly the concept of robust stability assessment (RSA), that could be integrated in dynamic security assessment packages and used in contingency screening and other planning and operational studies. [ABSTRACT FROM PUBLISHER]

An islanded microgrid consisting of grid-forming converters, being a high-order nonlinear system, exhibits rich nonlinear dynamical phenomena. The use of appropriate reduced-order models offers useful physical insights into the behavior of the system without the need for excessive computational resources. In this article, we derive a number of reduced-order models capable of describing the slow-scale dynamics of an islanded microgrid comprising a number of grid-forming converters. It is shown that slow-scale Hopf and homoclinic bifurcation behaviors arise from the stability of the voltage loops of grid-forming converters and are unrelated to the transmission network dynamics. Therefore, omitting the network dynamics does not affect the accuracy of reduced-order models in representing the slow-scale dynamics of the system. This is especially beneficial for modeling the microgrid with a complex transmission network. Furthermore, on this basis, all inner loops can be omitted when studying saddle-node bifurcation, leading to the development of power-flow-based reduced-order models. Finally, the stability of an islanded microgrid with a complex transmission network is evaluated. [ABSTRACT FROM AUTHOR]

This study aims to determine the galloping trend of iced transmission lines. A mathematical model considering the first three torsional modes is first established by applying the Galerkin method to the continuous dynamic model. The Hopf bifurcation theory is applied to the linear part of the mathematical model to calculate the critical stability conditions for each mode. Numerical procedures are then implemented on the mathematical model to simulate the galloping feature. An experiment on a continuous model for conductor galloping is designed to validate the above-mentioned galloping feature. The phenomena observed in the wind tunnel test are in good agreement with the theoretical observations. The results show that torsional galloping modifies the numbers of bifurcation points for the in-plane modes. A lower in-plane mode is gradually substituted by a higher one with increasing wind velocity. The theoretical and experimental results are then compared in terms of the galloping frequency and wind velocity range of galloping. By applying the experimental parameters to the theoretical model, the consistency between the theory and the experiment is proven. A convenient method is proposed to predict the wind speed range of galloping and is expected to be applicable for predictions of other critical parameters. [ABSTRACT FROM AUTHOR]

In this article, the slow-scale instability occurring in the three-level T-type inverter with a passive memristive (3LT2IPM) load is investigated. The average model of the 3LT2IPM, whose coefficient matrix is nonlinear periodic time-varying, is constructed, both harmonic balance method used to calculate the approximate solution of the average model and Floquet theory used to identify the circuit dynamic states are applied to explore the mechanism of the slow-scale instability emerging in the 3LT2IPM. Theoretical results indicate that the slow-scale instability of the 3LT2IPM is caused by Hopf bifurcation emerging in a region where the frequency is higher than line frequency but much lower than switching frequency. Also, the conditions of three theoretical parameters that make the theoretical analysis results as accurate as possible are presented. Different parameters impact on the stability boundary of the 3LT2IPM in various design parameter spaces are discussed, and the Floquet multiplier sensitivity is analyzed to identify key parameters for the stability of the 3LT2IPM, which are helpful to guide parameter adjustment of the 3LT2IPM to ensure its stable operation in practice. Finally, hardware experiment is established and experimental verification is provided. Physical experiments agree well with simulations, which together demonstrate the correctness of theoretical analysis. [ABSTRACT FROM AUTHOR]

Stochastic optimal power flow can provide the system operator with adequate strategies for controlling the power flow to maintain secure operation under stochastic parameter variations. One limitation of stochastic optimal power flow has been that only line flows have been used as security constraints. In many systems voltage stability and small-signal stability also play an important role in constraining the operation. [ABSTRACT FROM PUBLISHER]

Various indices are proposed and studied to detect and predict oscillatory instabilities associated with Hopf bifurcations (HBs) in power systems. A methodology is also presented to produce a linear profile for these indices. They are based on eigenvalue and singular values of the state and extended system matrices. Their application to several test power systems is presented to demonstrate their usefulness, particularly for online applications. [ABSTRACT FROM AUTHOR]

Coupled-core fluxgate magnetometer (CCFM), which is based on the coupling-induced oscillations in bistable nonlinear dynamics, can achieve self-excitation and obtain superior performances compared with the single core fluxgate magnetometer under the premise of utilizing the same residence times difference readout method. One of the pivotal factors determining the performances of CCFM is the critical coupling factor. To get control of it and further enhance the sensor performances, the negative feedback is exploited and implemented by feeding the magnetization from induction coil to excitation coil of the same fluxgate element (self-feedback). Theoretical analyses, Simulink simulations with a quantitative model, and experimental results obtained in the magnetic shielded environment reveal the critical coupling factor adjustment effect of negative feedback on CCFM and confirm the substantial enhancement of sensor performances. Finally, the sensitivity of CCFM for the static magnetic field detection is improved from 0.0253 to $0.7895~\mu \text{s}$ /nT, and the magnetic resolution of CCFM is optimized from 0.395 to 0.049 nT. Therefore, the negative feedback is an effective and reliable method for performances enhancement of CCFM, and it has potential utilization on the oscillation systems with similar dynamic peculiarities for factor adjustment. [ABSTRACT FROM AUTHOR]

The design of microgrids at the level of distribution systems requires a stable behavior for multiple operation states. The tools used to study the stability of such systems require the estimation of the grid impedance. By the use of the grid impedance estimation around an operation point, it is possible to define a space variable-parameter to obtain a qualitative or quantitative measure from the operation to the unstable boundary. This study presents a comparison of the Kalman filter and the recursive least squares method for the estimation of the grid impedance. The grid impedance is estimated by the technique based on two neighbor operation points. The results were validated by a hardware in the loop and an experimental setup. Finally, the estimated values of the grid impedance of a microgrid are used with a large signal stability study of a dc constant power load. [ABSTRACT FROM AUTHOR]

A new method is presented for the two-level harmonic-balance analysis of multivalued synchronized solution curves in injection-locked oscillators. The method is based on the extraction of a nonlinear admittance function, which describes the circuit response from the input source terminals. It does not require any optimization or parameter switching procedures, this constituting a significant advantage compared with previous analysis techniques. With additional mathematical conditions, it enables a straightforward determination of the turning point and Hopf bifurcation loci that delimit the stable injection-locked operation bands. The codimension two bifurcation point at which the turning point and Hopf bifurcation loci merge is analyzed in detail, as well as the saddle-connection locus. As it is shown, a second intersection of the saddle-connection locus with the turning point locus acts as a boundary between synchronization points and points associated with jumps and hysteresis. The likely observation of chaotic solutions in the neighborhood of the saddle-connection locus is discussed too. The techniques have been validated by application to several injection-locked oscillators, obtaining good agreement with the experimental results. [ABSTRACT FROM PUBLISHER]

In this letter, we study the effect of many body interactions on the collective response of confined electrons in doped quantum-well (QW) heterostructures to intense far-infrared radiation. Absorption lineshapes are computed both by numerically integrating the equations of motion and by using the appropriately time-averaged equations. For a two-subband double-QW system optical bistability is observed and its parameter range is given. For an asymmetric triple-QW structure driven at ω≈E2-E0 Hopf bifurcations occur which generate a strong response at a frequency incommensurate with the drive frequency or any natural frequency of the system [ABSTRACT FROM PUBLISHER]