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<jats:p>Optical fibers are seen in the optical sensing and optical fiber communication. Simultaneous propagation of optical pulses in an inhomogeneous optical fiber is described by a coupled time-dependent coefficient fourth-order nonlinear Schrödinger system, which is discussed in this paper. For such a system, we work out the Lax pair, Darboux transformation, and corresponding vector semi-rational nonautonomous rogue wave solutions. When the group velocity dispersion (GVD) and fourth-order dispersion (FOD) coefficients are the constants, we exhibit the first- and second-order vector semi-rational rogue waves which are composed of the four-petalled rogue waves and eye-shaped breathers. Both the width of the rogue wave along the time axis and temporal separation between the adjacent peaks of the breather decrease with the GVD coefficient or FOD coefficient. With the GVD and FOD coefficients as the linear, cosine, and exponential functions, we respectively present the first- and second-order periodic vector semi-rational rogue waves, first- and second-order asymmetry vector semi-rational rogue waves, and interactions between the eye-shaped breathers and the composite rogue waves.</jats:p>

<jats:p>We deal with the Wick-type stochastic fractional Korteweg de–Vries (KdV) equation with conformable derivatives. With the aid of the Exp-function method, white noise theory, and Hermite transform, we produce a novel set of exact soliton and periodic wave solutions to the fractional KdV equation with conformable derivatives. With the help of inverse Hermite transform, we get stochastic soliton and periodic wave solutions of the Wick-type stochastic fractional KdV equation with conformable derivatives. Eventually, by an application example, we show how the stochastic solutions can be given as Brownian motion functional solutions.</jats:p>

<jats:p>Laguerre polynomial’s photon-added squeezing vacuum state is constructed by operation of Laguerre polynomial’s photon-added operator on squeezing vacuum state. By making use of the technique of integration within an ordered product of operators, we derive the normalization coefficient and the calculation expression of 〈<jats:italic>a<jats:sup>l</jats:sup>a</jats:italic> <jats:sup>†</jats:sup>〉. Its statistical properties, such as squeezing, the anti-bunching effect, the sub-Poissonian distribution property, the negativity of Wigner function, <jats:italic>etc.</jats:italic>, are investigated. The influences of the squeezing parameter on quantum properties are discussed. Numerical results show that, firstly, the squeezing effect of the 1-order Laguerre polynomial’s photon-added operator exciting squeezing vacuum state is strengthened, but its anti-bunching effect and sub-Poissonian statistical property are weakened with increasing squeezing parameter; secondly, its squeezing effect is similar to that of squeezing vacuum state, but its anti-bunching effect and sub-Poissonian distribution property are stronger than that of squeezing vacuum state. These results show that the operation of Laguerre polynomial’s photon-added operator on squeezing vacuum state can enhance its non-classical properties.</jats:p>

<jats:p>We investigated the quantum speed limit time of a non-Hermitian two-level system for which gain and loss of energy or amplitude are present. Our results show that, with respect to two distinguishable states of the non-Hermitian system, the evolutionary time does not have a nonzero lower bound. The quantum evolution of the system can be effectively accelerated by adjusting the non-Hermitian parameter, as well as the quantum speed limit time can be arbitrarily small even be zero.</jats:p>

<jats:p>The characterization of an unknown quantum system requires the Hamiltonian identification. The full access to the system, however, is usually restricted, hindering the direct retrieval of the relevant parameters, and a reliable indirect estimation is usually required. In this work, based on the reformulated form of the original algorithm of Burgarth <jats:italic>et al.</jats:italic> [<jats:italic>Phys. Rev. A</jats:italic> <jats:bold>79</jats:bold> 020305 (2009)], the robustness of the estimation scheme against numerous sources of errors during the actual measurement is analyzed. The scheme is numerically studied for sites with a chain structure, exploring its applicability against observational errors including the limited signal-noise ratio and the finite spectral width. The spectral distribution of the end site is shown to determine the applicability of the method, and reducing the influence from truncated spectral components is critical to realize the robust reconstruction of the coupling strengths.</jats:p>

<jats:p>We find a new complex integration-transform which can establish a new relationship between a two-mode operator’s matrix element in the entangled state representation and its Wigner function. This integration keeps modulus invariant and therefore invertible. Based on this and the Weyl–Wigner correspondence theory, we find a two-mode operator which is responsible for complex fractional squeezing transformation. The entangled state representation and the Weyl ordering form of the two-mode Wigner operator are fully used in our derivation which brings convenience.</jats:p>

<jats:p>Chaotic encryption is one of hot topics in cryptography, which has received increasing attention. Among many encryption methods, chaotic map is employed as an important source of pseudo-random numbers (PRNS). Although the randomness and the butterfly effect of chaotic map make the generated sequence look very confused, its essence is still the deterministic behavior generated by a set of deterministic parameters. Therefore, the unceasing improved parameter estimation technology becomes one of potential threats for chaotic encryption, enhancing the attacking effect of the deciphering methods. In this paper, for better analyzing the cryptography, we focus on investigating the condition of chaotic maps to resist parameter estimation. An improved particle swarm optimization (IPSO) algorithm is introduced as the estimation method. Furthermore, a new piecewise principle is proposed for increasing estimation precision. Detailed experimental results demonstrate the effectiveness of the new estimation principle, and some new requirements are summarized for a secure chaotic encryption system.</jats:p>

<jats:p>To date, there are very few studies on the second Hopf bifurcation in a driven square cavity, although there are intensive investigations focused on the first Hopf bifurcation in literature, due to the difficulties of theoretical analyses and numerical simulations. In this paper, we study the characteristics of the second Hopf bifurcation in a driven square cavity by applying a consistent fourth-order compact finite difference scheme recently developed by us. We numerically identify the critical Reynolds number of the second Hopf bifurcation located in the interval of (11093.75,11094.3604) by bisection. In addition, we find that there are two dominant frequencies in its spectral diagram when the flow is in the status of the second Hopf bifurcation, while only one dominant frequency is identified if the flow is in the first Hopf bifurcation via the Fourier analysis. More interestingly, the flow phase portrait of velocity components is found to make transition from a regular elliptical closed form for the first Hopf bifurcation to a non-elliptical closed form with self-intersection for the second Hopf bifurcation. Such characteristics disclose flow in a quasi-periodic state when the second Hopf bifurcation occurs.</jats:p>

<jats:p>Previous studies have observed that electromagnetic induction can seriously affect the electrophysiological activity of the nervous system. Considering the role of astrocytes in regulating neural firing, we studied a simple neuron–astrocyte coupled system under electromagnetic induction in response to different types of external stimulation. Both the duration and intensity of the external stimulus can induce different modes of electrical activity in this system, and thus the neuronal firing patterns can be subtly controlled. When the external stimulation ceases, the neuron will continue to fire for a long time and then reset to its resting state. In this study, “delay” is defined as the delayed time from the firing state to the resting state, and it is highly sensitive to changes in the duration or intensity of the external stimulus. Meanwhile, the self-similarity embodied in the aforementioned sensitivity can be quantified by fractal dimension. Moreover, a hysteresis loop of calcium activity in the astrocyte is observed in the specific interval of the external stimulus when the stimulus duration is extended to infinity, since astrocytic calcium or neuron electrical activity in the resting state or during periodic oscillation depends on the initial state. Finally, the regulating effect of electromagnetic induction in this system is considered. It is clarified that the occurrence of “delay” depends purely on the existence of electromagnetic induction. This model can reveal the dynamic characteristics of the neuron–astrocyte coupling system with magnetic induction under external stimulation. These results can provide some insights into the effects of electromagnetic induction and stimulation on neuronal activity.</jats:p>

<jats:p>The phospholipid membrane plays a key role in myriad biological processes and phenomena, and the arrangement structure of membrane determines its function. However, the molecular arrangement structure of phospholipids in cell membranes is difficult to detect experimentally. On the basis of molecular dynamic simulations both in a non-destructive way and at native environment, we observed and confirmed that the phospholipids self-assemble to a hexagonal arrangement structure under physiological conditions. The underlying mechanism was revealed to be that there are hexagonal arrangement regions with a lower free energy around each lipid molecule. The findings potentially advance the understanding of biological functions of phospholipid bilayers.</jats:p>