查看更多>>摘要：Let N denote the set of all positive integers and let N-0 = N boolean OR{0}. For a strictly increasing sequence A of positive integers, let P(A) be the set of all integers which can be represented as the finite sum of distinct terms of A. Fix an integer b such that b is an element of {1, 2, 4, 7, 8} or b >= 11. For every integer k >= 1, define inductively c(k)((b)) as the smallest positive integer r so that there exist two strictly increasing sequences A = {a(i)}(i=1)(infinity) and B = {b(i)}(i=1)(infinity) 1 of positive integers such that (1) b1 = c(1)((b)), b(2) = c(2)((b))= 3b + 5; (2) bi = c(i)((b)) for all 3 <= i <= k - 1 and b(k) = r; (3) P(A) = N-0 \ {b(i) : i is an element of N} and a(i) <= Sigma(j<i) a(j) + 1 for all a(i) >= b + 1. Furthermore, let C(b) := {C-(b) : {c(k)((b))k is an element of N} and A((b)) := : A is a strictly increasing sequence of positive integers such that P(A) = N-0 \ C-(b). For any positive real number x, we let A(x) denote the number of terms no more than x in the sequence A and define L-x((b)) := min(A is an element of A(b)) A(x). In this paper, we determine the exact value of L-x((b)) for any positive real number x, and give a characterization on the strictly increasing sequence A of positive integers such that P(A) = N-0 \C-(b) and A(x) = L-x((P)) for any positive real number x >= c(1)((b)) -1. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：The different tem perature-dependent switchable thermal devices are designed in this paper, which can automatically realize the switchable thermal concentrating or cloaking functions at different temperature intervals. Based on the temperature-dependent transformation thermotics, we first theoretically derive the material parameters of the diamond shaped switchable thermal concentrators and cloaks in the transformed space, thus achieving the construction of the mathematical models of temperature-dependent switchable thermal concentrators and cloaks. Then, we further integrate the switchable thermal concentrating and cloaking functions described above into a single device to construct the path-dependent switchable devices, which can intelligently control the thermal concentrating and cloaking functions along different axes simultaneously as the temperature changes. Finally, the temperature-dependent properties of the switchable thermal concentrators, cloaks and path-dependent devices are validated numerically. The results show that the switchable thermal concentrators, cloaks, and path-dependent devices can perfectly realize the thermal concentrating, cloaking, and x-directional concentrating and y directional cloaking functions at specific different tem perature intervals, respectively. Once the specific temperature intervals have changed, the thermal bifunctions described above are turned off automatically. The temperature-dependent switchable properties can also be extended to other physical fields to design the intelligent multi-physical metadevices.(c) 2022 Elsevier Inc. All rights reserved.
Kavikumar, R.Kwon, O. M.Sakthivel, R.Lee, S. H....
18页
查看更多>>摘要：The composite fault-tolerant control problem for semi-Markov jumping nonlinear systems with time delays, uncertainties faults and multiple disturbances is addressed in this paper. The main intention of this work is to design a sliding mode control (SMC) law via an interval type-2 (IT2) fuzzy approach in such a way that it attenuates and rejects the impacts of uncertainty, nonlinearity, faults and external disturbances. Notably, first, an IT2 fuzzy disturbance observer is formulated to estimate the external disturbances and then an IT2 fuzzy fault diagnosis observer is designed to estimate the faults effectively. Next, a SMC-based fault-tolerant strategy is developed to compensate the diagnosed faults and disturbances satisfactorily. By using the linear matrix inequality and Lyapunov technique, the required stability constraints are developed with prescribed H-infinity performance index. The importance and effectiveness of the developed composite fault-tolerant control scheme are finally validated through two numerical examples. (c) 2022 Elsevier Inc. All rights reserved.
Li, Lin LinFerreira, Claudia PioAinseba, Bedreddine
19页
查看更多>>摘要：In this paper, we investigate the local exact controllability of an age structured problem modelling the ability of malaria vectors to shift their biting time to avoid the stressful environmental conditions generated by the use of indoor residual spraying (IRS) and insecticide-treated nets (ITNs). We establish a new Carleman's inequality for our age diffusive model with nonlocal birth process and periodic biting time boundary conditions. Some estimates of the theory of parabolic boundary value problems in L-k are used to get the controllability. (c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：A B S T R A C T Impulsive one-step numerical methods are defined in the present paper, especially, a common and widely used numerical form generalised from Runge-Kutta methods defined as impulsive Runge-Kutta methods. And it is proved that a consistent and zero-stable method thus convergent. Moreover, it is also proved that an impulsive one-step numerical method is convergent of order p if the corresponding method is pth order. Another equivalent form of impulsive one-step numerical methods are also introduced. In addition, numerical experiments are provided to illustrate the advantage of impulsive Runge-Kutta methods.(c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：This article is focused on studying the spatially extended reaction-diffusion system with a diagonal diffusion matrix in a bounded domain for a biophysically motivated excitable model. Diffusion induces spontaneous stationary patterns in the spatially extended homogeneous medium. We investigate the dynamics of the diffusively coupled network modulated by a Hindmarsh-Rose prototype model that describes the emergence of self-excited spiking activities with certain parameters and a constant injected stimulus. The linear stability analysis in this framework around the homogeneous steady states illustrates the emergence of stationary patterns. Turing domains are reported in the parameter space where Hopf bifurcation is determined. The bifurcation diagram helps us in understanding the transition mechanism in the spatial system. We have investigated the existence of Turing-Hopf bifurcation and established how Hopf and Turing curves divide the parameter space into three different dynamically significant regions. We have also studied the existence of Hopf bifurcation in the spatiotemporal system. Theoretically, the amplitude equations are derived by means of nonlinear multiple-scale analysis method and analyzed near the Hopf and Turing instabilities in the system. In particular, we observe asymptotic expressions for a wide range of various patterns (stationary, hexagonal, mixed-state) sustained by the spatial system. We obtain the explicit conditions to establish the structural transitions and stability of the diverse forms of these Turing patterns. These results reveal how the diffusive network evolves. To establish the results, the analytical derivations are demonstrated that are corroborated by numerical simulations of the corresponding diffusion induced system. Finally, we observe that the coupled excitable systems participate in a collective behavior that may contribute significantly to irregular neural dynamics associated with certain brain pathologies.(c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this research, considering the toxin avoidance effects of zooplankton to toxic phytoplankton in space as cross-diffusion terms, a modified model is proposed on the complex spatiotemporal dynamics of non-toxic phytoplankton, toxic phytoplankton and zooplankton system. In order to explore the toxin avoidance effects on pattern formation and selection, Turing bifurcation analysis and amplitude analysis are performed. The results of Turing analysis show that patterns can be formed when diffusion coefficient is less than a critical value. Amplitude equations are calculated and amplitude analysis show that stripe patterns, hexagon patterns and mixed patterns of stripes and hexagons can be theoretically predicted. Focusing on toxin avoidance coefficient (cross-diffusion coefficient) and diffusion coefficient of zooplankton, parameter space for pattern formation and selection is plotted. Numerical simulations on pattern formation are carried out to validate the theoretical analysis with five groups of parameters. With the increase of toxin avoidance effects, simulated patterns can be obtained as hexagons, mixed patterns of stripes and hexagons, stripes, mixed patterns of stripes and hexagons, and hexagons. Finally, taking stripe pattern as an example, simulated pattern is compared with predicted pattern. Simulation results are all consistent with theoretical analysis.(c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this paper, the problem of event-triggered finite-time trajectory tracking control for a quadrotor unmanned aerial vehicle (QUAV) is studied. For the translation and rotation subsystems of QUAV, the finite-time command filter can make the derivative of virtual control signals be quickly approximated, and the effect of filtered error is eliminated by constructing the fractional power error compensated mechanism. By synthesizing command filter technique and event-triggered mechanism into the framework of backstepping design procedure, the finite-time adaptive control strategy for a QUAV is proposed, which reduces the resource occupation and maintains the stability and performance. It is proved that the position and attitude tracking errors can converge to a small neighborhood near the origin in a finite time. Finally, the availability and superiority of the proposed finite-time algorithm are verified by a comparative simulation.(c) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：This work studies mainly the dissipative analysis issue of T-S fuzzy networked control systems (NCSs) with stochastic cyber-attacks (SCAs) and voluntary defense strategy (VDS), which has strong application background in the network information security field. Firstly, a novel time-delay-product relaxed condition (TDPRC) is introduced, which fully excavates time-varying delay (TVD) information in the established condition. Secondly, an improved boundary circulatory function (BLF) is developed, which takes advantage of the characteristics of the sampling moments. Here, when t is an element of [t(k), t(k+1) ), we only require Q(d(t)) to be an asymmetric matrix in V-c(x(t)). Then, a novel criterion and the corresponding control algorithm are developed by using reciprocally convex matrix inequality (RCMI), proper integral inequalities, and the linear convex combination method (LCCM). Furthermore, a new quantized sample-data and VDS controller under SCAs is established, which can prove that T-S fuzzy NCSs under a better dissipative index are asymptotically stable (AS). Lastly, a numerical simulation of the dynamic equation of truck-trailer system to certify the theory's feasibility and validity. (C) 2022 Elsevier Inc. All rights reserved.
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