Stable Parameter Region Research Articles

Phonon excitations of Floquet-driven superfluids in a tilted optical lattice

Tilted lattice potentials with periodic driving play a crucial role in the study of artificial gauge fields and topological phases with ultracold quantum gases. However, driving-induced heating and the growth of phonon modes restrict their use for probing interacting many-body states. Here, we experimentally investigate phonon modes and interaction-driven instabilities of superfluids in the lowest band of a shaken optical lattice. We identify stable and unstable parameter regions and provide a general resonance condition. In contrast to the high-frequency approximation of a Floquet description, we use the micromotion of the superfluids to analyze the growth of phonon modes from slow- to fast-driving frequencies. The model describes phonon excitations in both resonantly and nonresonantly driven systems, with or without a tilted potential. Our observations enable the prediction of stable parameter regimes for quantum-simulation experiments aimed at studying driven systems with strong interactions over extended time scales. Published by the American Physical Society 2024

Fractional-Order Modeling and Nonlinear Dynamic Analysis of Forward Converter

To accurately investigate the nonlinear dynamic characteristics of a forward converter, a fractional-order state-space averaged model of a forward converter in continuous conduction mode (CCM) is established based on the fractional calculus theory. And nonlinear dynamical bifurcation maps which use PI controller parameters and a reference current as bifurcation parameters are obtained. The nonlinear dynamic behavior is analyzed and compared with that of an integral-order forward converter. The results show that under certain operating conditions, the fractional-order forward converter exhibits bifurcations characterized by low-frequency oscillations and period-doubling as certain circuit and control parameters change. Under the same circuit conditions, there is a difference in the stable parameter region between the fractional and integral-order models of the forward converter. The stable zone of the fractional-order forward converter is larger than that of the integral-order one. Therefore, the circuit struggles to enter states of bifurcation and chaos. The stability domain for low-frequency oscillations and period-doubling bifurcations can be accurately predicted by using a small signal model and a predictive correction model of the fractional-order forward converter, respectively. Finally, by performing circuit simulations and hardware-in-the-loop experiments, the rationality and correctness of the theoretical analysis are verified.

A design methodology for nonlinear oscillator chains enabling energy localization tuning and soliton stability enhancement with optimal damping

In this paper, the vibration energy localization in coupled nonlinear oscillators is investigated, based on the creation of standing solitons. The main objective is to establish a design methodology for mechanical lattices using the Nonlinear Schrödinger Equation (NLSE) as a guide strategy, even in the presence of damping. A three-dimensional diagram is used to illustrate stable parameter regions for damped stationary solitons. Moreover, an analysis of the influence of the number of oscillators in the system, and a numerical investigation regarding the stability of solitonic behavior is done. Through numerical analyses, it is observed that the developed algorithm not only has the capability to locate the highest amplitudes in the chain of oscillators, but also to control the intensity at which these amplitudes are located according to design requirements. The outcomes of the proposed methodology elucidate the impact that the coupling stiffness has on the stabilization of the NLSE, as well as the influence of the number of oscillators on the continuity hypothesis. The developed algorithm holds potential for practical applications in mechanical engineering since the NLSE is used as a design line rather than as a consequence of the phenomenon description.

Interval analysis of the small‐signal stability of grid‐connected voltage‐source converter system considering multiparameter uncertainty

AbstractGrid‐connected voltage source converters (VSCs) have been broadly applied in modern power system. However, instability issues may be triggered by the integration of grid‐connected VSCs, jeopardising the operation of the power grid. Conventional stability analysis methods can be utilised to derive system stability margins under nominal conditions. Whereas grid‐connected VSCs inevitably operate under multiparameter uncertainty, which may result in overly optimistic or even incorrect estimations of stability margins, thereby posing potential risks to system operation. To address this issue, an interval small‐signal stability analysis approach is proposed to investigate the system stability under multiparameter uncertainty. First, the interval state‐space model of the grid‐connected VSC system is constructed based on interval symbolic linearisation. Furthermore, the interval eigenvalue decomposition is introduced to calculate the interval eigenvalue distribution of the interval state‐space model. Eventually, the upper bounds of the real part of the dominant interval eigenvalues are utilised for deriving interval stable parameter regions. Results of Monte Carlo analysis and time‐domain simulations of the grid‐connected VSC system are utilised to verify the effectiveness of the proposed interval stability analysis method.

Collective behavior of identical Stuart-Landau oscillators in a star network with coupling asymmetry effects.

In this study, we investigated the impact of the asymmetry of a coupling scheme on oscillator dynamics in a star network. We obtained stability conditions for the collective behavior of the systems, ranging from an equilibrium point over complete synchronization (CS) and quenched hub incoherence to remote synchronization states using both numerical and analytical methods. The coupling asymmetry factor α significantly influences and determines the stable parameter region of each state. For α ≠ 1, the equilibrium point can emerge when the Hopf bifurcation parameter a is positive, which is impossible for diffusive coupling. However, CS can occur even if a is negative under α < 1. Unlike diffusive coupling, we observe more behavior when α ≠ 1, including additional in-phase remote synchronization. These results are supported by theoretical analysis and validated through numerical simulations and independent of network size. The findings may offer practical methods for controlling, restoring, or obstructing specific collective behavior.

Inverse Design of Complex Block Copolymers for Exotic Self-Assembled Structures Based on Bayesian Optimization.

Variable chain topologies of multiblock copolymers provide great opportunities for the formation of numerous self-assembled nanostructures with promising potential applications. However, the consequent large parameter space poses new challenges for searching the stable parameter region of desired novel structures. In this Letter, by combining Bayesian optimization (BO), fast Fourier transform-assisted 3D convolutional neural network (FFT-3DCNN), and self-consistent field theory (SCFT), we develop a data-driven and fully automated inverse design framework to search for the desired novel structures self-assembled by ABC-type multiblock copolymers. Stable phase regions of three exotic target structures are efficiently identified in high-dimensional parameter space. Our work advances the new research paradigm of inverse design in the field of block copolymers.

A Generalization of Routh–Hurwitz Stability Criterion for Fractional-Order Systems with Order α ∈ (1, 2)

Based on the generalized Routh–Hurwitz criterion, we propose a sufficient and necessary criterion for testing the stability of fractional-order linear systems with order α∈1,2, called the fractional-order Routh–Hurwitz criterion. Compared with the existing criterion, ours involves fewer and simpler expressions, which is significant for analyzing the robust stability of high-dimensional uncertain systems. All these expressions are explicit ones about the coefficients of the characteristic polynomial of the system matrix, so the stable parameter region of fractional-order systems can be described directly. Some examples show the effectiveness of our method.

On the non-linear dynamics of vehicle shimmy coupled with handling motions: modelling, bifurcation analysis, and validations

A novel vehicle dynamic model considering the coupling mechanism between the front wheel shimmy and the vehicle lateral handling motions is established to investigate the interacting effect between the steering shimmy instability and the general motion instability, that focuses especially on the influence of the tyre force saturation induced by lateral-longitudinal coupling when different degrees and allocation strategy of braking force are applied. The typical 3-degree-of-freedom front wheel shimmy structure of dependent suspension is dynamically modelled by using the Lagrange method, alongside the equations for plane vehicle handling motions introduced. The stretched-string-based tyre kinematic equations, that describe the transient tyre-road contact status, are proposed by analytically deriving the coupling relations between the angular shimmy variables and vehicle motion status. A theoretically approximated linear tyre model, based on the coupling between vertical, longitudinal, and lateral directional forces, is analytically derived for stability analysis. Meanwhile, a complete PAC-2002 tyre model, with experimentally identified parameters, is employed for simulation verification. The stability chart of linear stability analysis shows the variation of the system bifurcation curves and stable parameter region under different parametric configurations, which gives that the degrees and allocations of braking force largely affect the stable parameter domain and the global stability. The variations of the system characteristic roots indicate that both Hopf and S-N bifurcation could happen due to shimmy oscillations and destabilization of motion, respectively, and their co-existence at certain parameter domains make the dynamic behaviour further unpredictable and complex. Numerical simulation verifies the dynamical characteristics of shimmy, and further analysis shows that three types of vehicle motion instability which coexisted with shimmy instability could be triggered by the coupling effect. In addition, the variation law of limit-cycle amplitude under varying vehicle driving inputs is summarized, and finally, a preliminary experiment is conducted for validations.

A parameter space method for analyzing Hopf bifurcation of fractional-order nonlinear systems with multiple-parameter

Hopf bifurcation analysis of fractional-order nonlinear systems with multiple-parameter is discussed in this paper. The regions and boundaries corresponding to Hopf bifurcation conditions are described in parameter space. Based on cylindrical algebraic decomposition, the parameter space is decomposed into finite number of connected regions by some boundaries. Then parameter space method is proposed to determine stable parameter region and Hopf bifurcation parameter hypersurface. One example illustrates the effectiveness of the method.

Medium Entropy Reduction and Instability in Stochastic Systems with Distributed Delay.

Many natural and artificial systems are subject to some sort of delay, which can be in the form of a single discrete delay or distributed over a range of times. Here, we discuss the impact of this distribution on (thermo-)dynamical properties of time-delayed stochastic systems. To this end, we study a simple classical model with white and colored noise, and focus on the class of Gamma-distributed delays which includes a variety of distinct delay distributions typical for feedback experiments and biological systems. A physical application is a colloid subject to time-delayed feedback control, which is, in principle, experimentally realizable by co-moving optical traps. We uncover several unexpected phenomena in regard to the system’s linear stability and its thermodynamic properties. First, increasing the mean delay time can destabilize or stabilize the process, depending on the distribution of the delay. Second, for all considered distributions, the heat dissipated by the controlled system (e.g., the colloidal particle) can become negative, which implies that the delay force extracts energy and entropy of the bath. As we show here, this refrigerating effect is particularly pronounced for exponential delay. For a specific non-reciprocal realization of a control device, we find that the entropic costs, measured by the total entropy production of the system plus controller, are the lowest for exponential delay. The exponential delay further yields the largest stable parameter regions. In this sense, exponential delay represents the most effective and robust type of delayed feedback.

Controlling stable tunneling in a non-Hermitian spin–orbit coupled bosonic junction

In this paper, we study how to apply a periodic driving field to control stable spin tunneling in a non-Hermitian spin–orbit (SO) coupled bosonic double-well system. By means of a high-frequency approximation, we obtain the analytical Floquet solutions and their associated quasienergies and thus construct the general non-Floquet solutions of the dissipative SO coupled bosonic system. Based on detailed analysis of the Floquet quasienergy spectrum, the profound effect of system parameters and the periodic driving field on the stability of spin-dependent tunneling is investigated analytically and numerically for both balanced and unbalanced gain–loss between two wells. Under balanced gain and loss, we find that the stable spin-flipping tunneling is preferentially suppressed with the increase of gain–loss strength. When the ratio of Zeeman field strength to periodic driving frequency Ω/ω is even, there is a possibility that continuous stable parameter regions will exist. When Ω/ω is odd, nevertheless, only discrete stable parameter regions are found. Under unbalanced gain and loss, whether Ω/ω is even or odd, we can get parametric equilibrium conditions for the existence of stable spin tunneling. The results could be useful for the experiments of controlling stable spin transportation in a non-Hermitian SO coupled system.

The effects of the FOPI controller and time delay on stability region of the fuel cell microgrid

In this paper, the effects of the time delay (τ) and the order of the fractional integral (λ) on the stable parameter region of the FOPI controller for a fuel cell microgrid is investigated. The stability boundary curves depending on λ and τ values of the fuel cell microgrid, i.e., stable parameters space of the FOPI controller, are obtained by using the stability boundary locus (SBL) method. The SBL is a graphical technique and in this technique, the stable regions of the system are obtained by using the characteristic equation of the system. The obtained stable regions are tested by the time-domain simulations and the generalized and modified Mikhailov (GMM) criterion. The effect of τ and λ on the stable parameter region of the FOPI controller for a fuel cell microgrid with time delay has been shown in the literature for the first time through this study. The obtained results show that τ and λ have considerable effects on the change of stable region. The results also show that the effect of λ is much higher than the τ′s effect. Therefore, it has been demonstrated that the effect of the large time delay, which makes the system unstable, can be reduced by λ in this study.

Jacobi analysis for an unusual 3D autonomous system

Little seems to be known about the study of the chaotic system with only Lyapunov stable equilibria from the perspective of differential geometry. Therefore, this paper presents Jacobi analysis of an unusual three-dimensional (3D) autonomous chaotic system. Under certain parameter conditions, this system has positive Lyapunov exponents and only two linear stable equilibrium points, which means that chaotic attractor and Lyapunov stable equilibria coexist. The dynamical behavior of the deviation vector near the whole trajectories (including all equilibrium points) is analyzed in detail. The results show that the value of the deviation curvature tensor at equilibrium points is only related to parameters; the two equilibrium points of the system are Jacobi stable if the parameters satisfy certain conditions. Particularly, for a specific set of parameters, the linear stable equilibrium points of the system are always Jacobi unstable. A periodic orbit that is Lyapunov stable is also proven to be always Jacobi unstable. Next, Jacobi-stable regions of the Lorenz system, the Chen system and the system under study are compared for specific parameters. It can be found that although these three chaotic systems are very similar, their regions of Jacobi stable parameters are much different. Finally, by comparing Jacobi stability with Lyapunov stability, the obtained results demonstrate that the Jacobi stable parameter region is basically symmetric with the Lyapunov stable parameter region.

A CAD-based Algorithm for Solving Stable Parameter Region of Fractional-order Systems with Structured Perturbations

Abstract Based on cylindrical algebraic decomposition (CAD) technique, an algorithm for solving the stable parameter region of factional-order systems with structured perturbations (FOSSP) is presented. The algorithm is nonconservative and universal for fractional order systems with order 0 &lt; α &lt; 2. And the computational complexity of the algorithm is less than existing methods. Two examples are given to show the effectiveness of the proposed method.

Prey-Predator Interactions in Two and Three Species Population Models

Discrete nonlinear two and three species prey-predator models are considered. Focus is on stability and nonstationary behaviour. Regarding the two species model, depending on the fecundity of the predator, we show that the transfer from stability to instability goes through either a supercritical flip or a supercritical Neimark-Sacker bifurcation and moreover that there exist multiple attractors in the chaotic regime, one where both species coexist and another where the predator population has become extinct. Sizes of basin of attraction for these possibilities are investigated. Regarding the three species models, we show that the dynamics may differ whether both predators prey upon the prey or if the top predator preys upon the other predator only. Both the sizes of stable parameter regions as well as the qualitative structure of attractors may be different.

An Explicit Method for Stability Analysis of 2D Systems Described by Transfer Function

In this paper, we propose a method to test the stability of two-dimensional (2D) linear discrete systems described by transfer function. And a complete region of disturbance parameters is solved to ensure the considered system with perturbations stability. Different from any other traditional algebraic methods, the algorithm of this method is explicit, which a large number of higher-order polynomial iterative operation doesn’t need to be carried out. By the fractional linear transformations, new condition is given in Hurwitz theorem, which doesn’t involve fractional calculation. The method is non-conservative for stability analysis and solving stable parameter region of 2D systems. It simplifies some existing methods. The computational cost is reduced. And it is better to solve the stability problems for 2D systems with disturbances. Examples illustrate the efficiency for testing the stability of higher-order 2D system and solving the robust stability problem of uncertain 2D systems.

Nonlinear modeling and stability analysis of a pilot-operated valve-control hydraulic system

A nonlinear dynamic model is developed to analyze the stability of a pilot-operated valve-control hydraulic system. The dynamic model includes motion of the valve spool and fluid dynamics in the system. Characteristics such as pressure flow across the valve port and orifices, pressure, and flow rate in valve chambers are taken into consideration. Bifurcation analysis is proposed and examined by numerical simulation results when the feedback orifice diameter changes. The effects of different system parameters such as pilot-operating pressure, spring stiffness, and overlap of inlet port on the stability border of the system are studied by two-dimensional bifurcation analyses. The study identifies that bifurcation can occur in the system and lead to sustained self-excited vibration with parameters in certain region of the parameter space. It suggests that the vibration can be effectively predicted and prevented by selecting system parameters from the asymptotic stable parameter region.

Population dynamics with multiple Allee effects induced by fear factors – A mathematical study on prey-predator interactions

• Mathematical models on effect of fear and strong Allee mechanism have been proposed and analysed. • We have shown how fear can significantly reduce the per-capita growth rate of prey with generalised predator. • We have shown that fear has no role in the stability of prey-predator system, with linear functional response. • Fear effect can stabilize the eco-epidemiological system and promote the coexistence of all the three populations. • Finally, fear may be a cause of the Allee effect/multiple Allee effects at low population density. In the present, ecologists generally consider the interactions, which are directly related to the density effects, that species have on each other, like predation, mutualism, refuge, etc. However, some experimental studies showed that apart from the direct killing, predation fears itself can reduce the prey growth rate by 40%. Therefore, in the present study, we have considered a trait effect, which is characterized by the reduction of prey growth rate due to fear of predator, where the prey is already suffered by the mating induced strong Allee effects, in the reproduction process. First, we developed and analyzed the single-species model and showed that how the fear effect can significantly reduce the per-capita growth rate (pgr) and may be a possible cause of the multiple Allee effects at low population density. Next, we consider a prey-predator model with linear functional response and showed that fear does not affect the equilibrium stability, but the time scale difference among two populations has a positive effect. It will help the system to converge to the stable steady states faster than before. Finally, we study an eco-epidemiological model with the same assumptions, where prey is being suffered by the disease. We showed that in eco-epidemiological systems fear can greatly affect the system stability. Fear can stabilize the system at the interior equilibrium, where all the three population coexists, or it can create the oscillatory coexistence of all the three populations. In the presence of fear, system shows bi-stability among different equilibria. We have also shown the basin stability at multiple stable parameter regions, which yields the probability of convergence of each equilibrium for a given set of different initial conditions. All these findings may have potential impacts in population management and conservation biology.

On the tertiary instability formalism of zonal flows in magnetized plasmas

This paper investigates the so-called tertiary instabilities driven by the zonal flow in gyro-kinetic tokamak core turbulence. The Kelvin Helmholtz instability is first considered within a 2D fluid model and a threshold in the zonal flow wave vector kZF&amp;gt;kZF,c for instability is found. This critical scale is related to the breaking of the rotational symmetry by flux-surfaces, which is incorporated into the modified adiabatic electron response. The stability of undamped Rosenbluth-Hinton zonal flows is then investigated in gyro-kinetic simulations. Absolute instability, in the sense that the threshold zonal flow amplitude tends towards zero, is found above a zonal flow wave vector kZF,cρi≈1.3 (ρi is the ion thermal Larmor radius), which is comparable to the 2D fluid results. Large scale zonal flows with kZF&amp;lt;kZF,c are unstable for sufficiently large amplitudes with increasing trend for an increasing radial scale. However, the critical E × B-shearing rate associated with the stability boundary ωE×B,c exceeds typical values connected to the pure flow state at marginal stability by more than an order of magnitude, which therefore lies deeply in the stable parameter region. Furthermore, the impact of zonal temperature perturbations on the tertiary instability is examined. Although temperature perturbations favor instability, the realistic values of gradient-driven gyro-kinetic simulations still lie deeply in the stable parameter regime. Therefore, the relevance of the tertiary instability as a saturation mechanism to the zonal flow amplitude is questioned, as most of the zonal flow intensity is concentrated in modes satisfying kZF≪kZF,c as well as ωE×B≪ωE×B,c. At the request of the authors, this article is being retracted effective 11 June 2020.

Constructing Hopf bifurcation lines for the stability of nonlinear systems with two time delays.

Although the plethora real-life systems modeled by nonlinear systems with two independent time delays, the algebraic expressions for determining the stability of their fixed points remain the Achilles' heel. Typically, the approach for studying the stability of delay systems consists in finding the bifurcation lines separating the stable and unstable parameter regions. This work deals with the parametric construction of algebraic expressions and their use for the determination of the stability boundaries of fixed points in nonlinear systems with two independent time delays. In particular, we concentrate on the cases for which the stability of the fixed points can be ascertained from a characteristic equation corresponding to that of scalar two-delay differential equations, one-component dual-delay feedback, or nonscalar differential equations with two delays for which the characteristic equation for the stability analysis can be reduced to that of a scalar case. Then, we apply our obtained algebraic expressions to identify either the parameter regions of stable microwaves generated by dual-delay optoelectronic oscillators or the regions of amplitude death in identical coupled oscillators.