Fuzzy Membership Function Dependent Switched Control for Nonlinear Systems with Memory Sampled-Data Information

In this paper, a fuzzy memory-based coupling sampled-data control (SDC) is designed for nonlinear systems through the switched approach. Compared with the usual SDC scheme, by employing the Bernoulli sequence, a more general coupling switched SDC that involving the signal transmission delay is designed. The Lyapunov-Krasovskii Functional (LKF) is presented with the available characteristics of the membership function, and a coupling sampling pattern, for the T-S fuzzy systems. Based on LKF, together with time derivative information of membership function, and the generalized N -order free-matrix-based inequality, the suitable conditions are obtained in terms of linear matrix inequalities (LMIs) for guaranteeing the asymptotic stability and stabilization of the concerned system. Then the desired fuzzy coupling SDC gain is attained from the solvable LMIs. In the end, two examples are given to validate the derived theoretical results.

Formulation of Time-Fractional Electrodynamics Based on Riemann-Silberstein Vector

In this paper, the formulation of time-fractional (TF) electrodynamics is derived based on the Riemann-Silberstein (RS) vector. With the use of this vector and fractional-order derivatives, one can write TF Maxwell’s equations in a compact form, which allows for modelling of energy dissipation and dynamics of electromagnetic systems with memory. Therefore, we formulate TF Maxwell’s equations using the RS vector and analyse their properties from the point of view of classical electrodynamics, i.e., energy and momentum conservation, reciprocity, causality. Afterwards, we derive classical solutions for wave-propagation problems, assuming helical, spherical, and cylindrical symmetries of solutions. The results are supported by numerical simulations and their analysis. Discussion of relations between the TF Schrödinger equation and TF electrodynamics is included as well.

Room-temperature single-photon source with near-millisecond built-in memory

Non-classical photon sources are a crucial resource for distributed quantum networks. Photons generated from matter systems with memory capability are particularly promising, as they can be integrated into a network where each source is used on-demand. Among all kinds of solid state and atomic quantum memories, room-temperature atomic vapours are especially attractive due to their robustness and potential scalability. To-date room-temperature photon sources have been limited either in their memory time or the purity of the photonic state. Here we demonstrate a single-photon source based on room-temperature memory. Following heralded loading of the memory, a single photon is retrieved from it after a variable storage time. The single-photon character of the retrieved field is validated by the strong suppression of the two-photon component with antibunching as low as $${g}_{{\rm{RR| W = 1}}}^{(2)}=0.20\pm 0.07$$ g RR∣W=1 ( 2 ) = 0.20 ± 0.07 . Non-classical correlations between the heralding and the retrieved photons are maintained for up to $${\tau }_{{\rm{NC}}}^{{\mathcal{R}}}=(0.68\pm 0.08)\ {\rm{ms}}$$ τ NC R = ( 0.68 ± 0.08 ) ms , more than two orders of magnitude longer than previously demonstrated with other room-temperature systems. Correlations sufficient for violating Bell inequalities exist for up to τBI = (0.15 ± 0.03) ms.

Analysis of the spread of COVID-19 in Morocco based on a SEIR epidemic model

Fractional calculus has been widely used in mathematical modeling of evolutionary systems with memory effect on dynamics. In order to illustrate the efficiency of this non-integer order calculus, we employ SEIR models to model the dynamics, with and without memory, of the spread of Covid-19 in Morocco country.

Dissipative structure and asymptotic profiles for symmetric hyperbolic systems with memory

We study symmetric hyperbolic systems with memory-type dissipation and investigate their dissipative structures under Craftsmanship condition. We treat two cases: memory-type diffusion and memory-type relaxation, and observe that the dissipative structures of these two cases are essentially different. Namely, we show that the dissipative structure of the system with memory-type diffusion is of the standard type, while that of the system with memory-type relaxation is of the regularity-loss type. Moreover, we investigate the asymptotic profiles of the solutions for [Formula: see text]. In the diffusion case, it is proved that the systems with memory and without memory have the same asymptotic profile for [Formula: see text], which is given by the superposition of linear diffusion waves. We have the same result also in the relaxation case under enough regularity assumption on the initial data.

Quantum Maps with Memory from Generalized Lindblad Equation

In this paper, we proposed the exactly solvable model of non-Markovian dynamics of open quantum systems. This model describes open quantum systems with memory and periodic sequence of kicks by environment. To describe these systems, the Lindblad equation for quantum observable is generalized by taking into account power-law fading memory. Dynamics of open quantum systems with power-law memory are considered. The proposed generalized Lindblad equations describe non-Markovian quantum dynamics. The quantum dynamics with power-law memory are described by using integrations and differentiation of non-integer orders, as well as fractional calculus. An example of a quantum oscillator with linear friction and power-law memory is considered. In this paper, discrete-time quantum maps with memory, which are derived from generalized Lindblad equations without any approximations, are suggested. These maps exactly correspond to the generalized Lindblad equations, which are fractional differential equations with the Caputo derivatives of non-integer orders and periodic sequence of kicks that are represented by the Dirac delta-functions. The solution of these equations for coordinates and momenta are derived. The solutions of the generalized Lindblad equations for coordinate and momentum operators are obtained for open quantum systems with memory and kicks. Using these solutions, linear and nonlinear quantum discrete-time maps are derived.