The Consensus of Different Fractional-Order Chaotic Multiagent Systems Using Adaptive Protocols

This paper is concerned with the adaptive consensus problem of incommensurate chaotic fractional order multiagent systems. Firstly, we introduce fractional-order derivative in the sense of Caputo and the classical stability theorem of linear fractional order systems; also, algebraic graph theory and sufficient conditions are presented to ensure the consensus for fractional multiagent systems. Furthermore, adaptive protocols of each agent using local information are designed and a detailed analysis of the leader-following consensus is presented. Finally, some numerical simulation examples are also given to show the effectiveness of the proposed results.

Physics-based control of neoclassical tearing modes on TCV

This paper presents recent progress on the studies of neoclassical tearing modes (NTMs) on TCV, concerning the new physics learned and how this physics contributes to a better real-time (RT) control of NTMs. A simple technique that adds a small (sinusoidal) sweeping to the target electron cyclotron (EC) beam deposition location has proven effective both for the stabilization and prevention of 2⁄1 NTMs. This relaxes the strict requirement on beam-mode alignment for NTM control, which is difficult to ensure in RT. In terms of the EC power for NTM stabilization, a control scheme making use of RT island width measurements has been tested on TCV. NTM seeding through sawtooth (ST) crashes or unstable current density profiles (triggerless NTMs) has been studied in detail. A new NTM prevention strategy utilizing only transient EC beams near the relevant rational surface has been developed and proven effective for preventing ST-seeded NTMs. With a comprehensive modified Rutherford equation (co-MRE) that considers the classical stability both at zero and finite island width, the prevention of triggerless NTMs with EC beams has been simulated for the first time. The prevention effects are found to result from the local effects of the EC beams (as opposed to global current profile changes), as observed in a group of TCV experiments scanning the deposition location of the preemptive EC beam. The co-MRE has also proven able to reproduce well the island width evolution in distinct plasma scenarios on TCV, ASDEX Upgrade and MAST, with very similar constant coefficients. The co-MRE has the potential of being applied in RT to provide valuable information such as the EC power required for NTM control with RT-adapted coefficients, contributing to both NTM control and integrated control with a limited set of actuators.

Stabilization of Microbial Communities by Responsive Phenotypic Switching

Clonal microbes can switch between different phenotypes and recent theoretical work has shown that stochastic switching between these subpopulations can stabilize microbial communities. This phenotypic switching need not be stochastic, however, but can also be in response to environmental factors, both biotic and abiotic. Here, motivated by the bacterial persistence phenotype, we explore the ecological effects of such responsive switching by analyzing phenotypic switching in response to competing species. We show how the stability of microbial communities with responsive switching differs generically from that of communities with stochastic switching only. To understand this effect, we go on to analyse simple two-species models. Combining exact results and numerical simulations, we extend the classical stability results for models of two competing species without phenotypic variation to the case where one of the two species switches, stochastically and responsively, between two phenotypes. In particular, we show that responsive switching can stabilize coexistence even when stochastic switching on its own does not affect the stability of the community.

Entrainment and growth of vortical disturbances in the channel-entrance region

The entrainment of free-stream unsteady three-dimensional vortical disturbances in the entry region of a channel is studied via matched asymptotic expansions and by numerical means. The interest is in flows at Reynolds numbers where experimental studies have documented the occurrence of intense transient growth, despite the flow being stable according to classical stability analysis. The analytical description of the vortical perturbations at the channel mouth reveals how the oncoming disturbances penetrate into the wall-attached shear layers and amplify downstream. The effects of the channel confinement, the streamwise pressure gradient and the viscous/inviscid interplay between the oncoming disturbances and the boundary-layer perturbations are discussed. The composite perturbation velocity profiles are employed as initial conditions for the unsteady boundary-region perturbation equations. At a short distance from the channel mouth, the disturbance flow is mostly confined within the shear layers and assumes the form of streamwise-elongated streaks, while farther downstream the viscous disturbances permeate the whole channel although the base flow is still mostly inviscid in the core. Symmetrical disturbances exhibit a more significant growth than anti-symmetrical disturbances, the latter maintaining a nearly constant amplitude for several channel heights downstream before growing transiently, a unique feature not reported in open boundary layers. The disturbances are more intense as the frequency decreases or the bulk Reynolds number increases. We compute the spanwise wavelengths that cause the most intense downstream growth and the threshold wall-normal wavelengths below which the perturbations are damped through viscous dissipation.

On the equilibrium bifurcation of axially deformable holonomic systems: solution of a long-standing enigma

The stability of equilibrium is a fundamental topic in mechanics and applied sciences. Apart from its central role in most engineering fields, it also arises in many natural systems at any scale, from folding/unfolding processes of macromolecules and growth-induced wrinkling in biological tissues to meteorology and celestial mechanics. As such, a few key models represent essential benchmarks in order to gain significant insights into more complex physical phenomena. Among these models, a cornerstone is represented by a structure made of two straight axially deformable bars, connected by an elastic hinge and simply supported at the ends, which are capable of buckling under a compressive axial force. This classical example has been proposed and analysed in some depth by Feodosyev but the attention is here focused on an apparently paradoxical result given by this model, i.e. the existence of a lower bound for the axial-to-flexural stiffness ratio in order for the bifurcation to take place. This enigma is solved theoretically by showing that, differently from other classical stability problems, constitutive and geometric nonlinearities cannot be a priori disconnected and an ideal linearized axial constitutive law cannot be employed in this case. The theory is validated with an experiment, and post-buckling and energy extrema of the proposed solution are discussed as well, highlighting possible snap-back and snap-through phenomena. Finally, the results are extended to the complementary case of tensile buckling.

Classical Theory of Linear Multistep Methods for Volterra Functional Differential Equations

Based on the linear multistep methods for ordinary differential equations (ODEs) and the canonical interpolation theory that was presented by Shoufu Li who is exactly the second author of this paper, we propose the linear multistep methods for general Volterra functional differential equations (VFDEs) and build the classical stability, consistency, and convergence theories of the methods. The methods and theories presented in this paper are applicable to nonneutral, nonstiff, and nonlinear initial value problems in ODEs, Volterra delay differential equations (VDDEs), Volterra integro-differential equations (VIDEs), Volterra delay integro-differential equations (VDIDEs), etc. At last, some numerical experiments verify the correctness of our theories.

Characterization of the dissipative structure for the symmetric hyperbolic system with non-symmetric relaxation

This paper is concerned with the dissipative structure for the linear symmetric hyperbolic system with non-symmetric relaxation. If the relaxation matrix of the system has symmetric property, Shizuta and Kawashima in 1985 introduced the suitable stability condition called Classical Stability Condition in this paper, and Umeda, Kawashima and Shizuta in 1984 analyzed the dissipative structure of the standard type. On the other hand, Ueda, Duan and Kawashima in 2012 and 2018 focused on the system with non-symmetric relaxation, and got the partial result which is the extension of known results. Furthermore, they argued the new dissipative structure called the regularity-loss type. In this situation, our purpose of this paper is to extend the stability theory introduced by Shizuta and Kawashima in 1985 and Umeda, Kawashima and Shizuta in 1984 for our general system.

Variations on Lyapunov's stability criterion and periodic prey-predator systems

<p style='text-indent:20px;'>A classical stability criterion for Hill's equation is extended to more general families of periodic two-dimensional linear systems. The results are motivated by the study of mechanical vibrations with friction and periodic prey-predator systems.</p>

Comments on the stability of the KPV state

Using the blackfold approach, we study the classical stability of the KPV (Kachru-Pearson-Verlinde) state of anti-D3 branes at the tip of the Klebanov-Strassler throat. With regards to generic long-wavelength deformations considered, we found no instabilities. We comment on the relation of our results to existing results on the stability of the KPV state.

Inflation of universe by nonlinear electrodynamics

Nonlinear electrodynamics with two-dimensional parameters is studied. The range of electromagnetic fields, when principles of causality, unitarity and the classical stability hold, are obtained. A singularity of the electric field at the center of charges is absent within our model and there are corrections to the Coulomb law as [Formula: see text]. The universe inflation takes place in the background of stochastic magnetic fields. The second stage of the universe evolution is the radiation era so that the graceful exit exists. We estimated the spectral index, the tensor-to-scalar ratio, and the running of the spectral index that are in a rough accordance with the PLANCK and WMAP data.