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This article investigates the issue of anti‐modal‐asynchrony sliding mode control (SMC) for discrete semi‐Markov jump systems with bi‐boundary sojourn time. Asynchronous mechanism refers to the mismatch phenomenon between the system mode and the controller mode, in which the modal lag is mode‐dependent to reduce some conservatism compared with traditional mode‐independent lag. In contrast to traditional semi‐Markov jump systems, the sojourn time of each mode in this article is considered to have upper‐and‐lower bounds, representing better characteristics than the upper bound. Based on the semi‐Markov kernel and the Lyapunov function related to the elapsed time of current mode, a sufficient condition is proposed to ensure that the mean‐square stability of the underlying system is achieved under an equivalent SMC mechanism. The conditions for the existence of the designed controller are obtained, which shows that the constructed SMC mechanism is effective against asynchronous mode jumps. An anti‐modal‐asynchrony SMC mechanism is constructed to achieve the reachability of discrete quasi‐sliding mode. Finally, the F‐404 aircraft engine model is given to validate the effectiveness of the control strategy. [ABSTRACT FROM AUTHOR]

In this study, we consider a diffusion system of the Keller-Segel type, which is pivotal in describing the underlying mechanisms of pattern formation. First, the heteroclinic orbit for the degenerate case is investigated by constructing an invariant region. Furthermore, the persistence of travelling waves in Keller-Segel systems in the presence of local or nonlocal delay is respectively established. The geometric singular perturbation theory along with Fredholm theory are the foundational analytical tools utilized in this study. Eventually, the asymptotic behaviors of the travelling waves are elucidated, offering new insights into their dynamic properties. [ABSTRACT FROM AUTHOR]

This research paper introduces a novel approach to deriving traveling wave solutions (TWSs) for the Caputo-fractional Klein–Gordon equations. This research presents a distinct methodological advancement by introducing TWSs of a particular time-fractional partial differential equation, utilizing a non-local fractional operator, specifically the Caputo derivative. To achieve our goal, a novel transformation is considered, that converts a time-fractional partial differential equation into fractional ordinary differential equations, enabling analytical solutions through various analytical methods. This paper employs the homotopy analysis method to achieve the target objectives. To demonstrate the efficiency and applicability of the proposed transform and method, two examples are discussed and analyzed in figures. [ABSTRACT FROM AUTHOR]

In this paper, we present a new encryption method based on discrete wavelet transform (DWT). This method provides a number of advantages as a pseudo randomness and sensitivity due to the variation of the initial values. We start by decomposing the image with spatial reconstruction by DWT, followed by preformation by fractional chaotic cryptovirology and Henon map keys for space encryption. Bearing in mind the rapid pace of change in the fields of fractional chaotic cryptovirology, our findings suggest that the proposed method is too powerful relative to the key sensitivity, histogram, entropy and correlation coefficient. [ABSTRACT FROM AUTHOR]

Summary: In this paper, a generalized sliding event‐triggered control for the closed‐loop Markov switching systems (CLMSSs) is studied. It is proved that the system is driven to the designed sliding mode surface under a given sliding mode controller. A generalized sliding event‐triggered controller is developed to obtain strictly (풬,풮,ℛ)−γ−dissipative performance of CLMSSs, in which the combination of sliding mode control and event‐triggering protocol makes the control performance more efficient and generalized. Further, two dissipative criteria for CLMSSs are established. Finally, the results of numerical simulations give a witness for the effectiveness of the given theorems and methods. [ABSTRACT FROM AUTHOR]

We investigate some new aspects of the nonlinear interaction between a three-level Ξ -type atom and bimodal field. The photon-assisted atomic phase damping, detuning parameter, Kerr nonlinearity and the time-dependent coupling have been considered. The general solution has been obtained by using the Schrődinger equation when the atom and the field are initially prepared in the excited state and coherent state, respectively. The atomic population inversion and concurrence are discussed. It is shown that the time-dependent coupling parameter and the detuning parameter can be considered as quantum controller parameters of the atomic population inversion and quantum entanglement in the considered model. [ABSTRACT FROM AUTHOR]

In this article we suggest the entire functions associated with the L-functions attached to cusp forms. The entire function defined by the Fourier cosine transform is the solution for the diffusion equation in 1-D case. We propose three conjectures for the zeros of three entire functions of order one via theory of entire functions. [ABSTRACT FROM AUTHOR]

In this article we suggest a new odd entire function of order one. We discover that it is the solution of the heat equation. We propose a new conjecture that this function has only real zeros. The obtained result gives a connection with the heat problem and number theory. [ABSTRACT FROM AUTHOR]

We introduce a new framework for quantum two-spin correlations based on a quantum skew information quantity and long-negativity. The quantum correlations for an anisotropic two-qubit Heisenberg X Y Z model are affected by physical parameters such as intrinsic decoherence, Werner states and time-dependent magnetic fields. In particular, the joint effects of Werner states, magnetic fields and anisotropic parameters on quantum correlation robustness are investigated in the presence of intrinsic decoherence. For an initially uncorrelated state, robust entanglement is generated while skew information between the two quantum bits no longer exists. It is shown that the magnetic field makes the system strongly correlated with incredibly significant steady-state values in uncorrelated states. The phenomenon of sudden death and sudden birth appear during the evolution process of initial conditions. Finally, if the system starts from a mixed state or a Werner state, the magnetic field does not play a significant role in the monotonically decreasing correlations. By leveraging our framework, one can create a kind of stability between the uncertainty-induced quantum nonlocality and the local quantum uncertainty correlations. [ABSTRACT FROM AUTHOR]

This article mainly concentrates on the synchronization problem for a more general kind of the master–slave memristor-based neural networks with fractional derivative. By applying a continuous-frequency-distributed equivalent model tool, some new outcomes and sufficient conditions on the robust synchronization of the master–slave neural networks with uncertainty are proposed via linear matrix inequality (LMI). Finally, two memristive neural networks model with fractional derivatives are presented to validate the efficiency of the theoretical results. [ABSTRACT FROM AUTHOR]