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<jats:p>We study dynamical behaviors of a Bose–Einstein condensate (BEC) containing a dark soliton reflected from potential wells and potential barriers, respectively. The orientation angle of the dark soliton and the width of the potential change play key roles on the reflection probability <jats:italic>R</jats:italic> <jats:sub>s</jats:sub>. Variation of the reflection probability with respect to the orientation angle <jats:italic>θ</jats:italic> of the dark soliton can be well described by a cosine function <jats:italic>R</jats:italic> <jats:sub>s</jats:sub> ∼ cos [<jats:italic>λ</jats:italic>(<jats:italic>θ</jats:italic> – <jats:italic>π</jats:italic>/2)], where <jats:italic>λ</jats:italic> is a parameter determined by the width of the potential change. There are two characteristic lengths which determine the reflection properties. The dependence of the reflection probability on the width of the potential change shows distinct characters for potential wells and potential barriers. The length of the dark soliton determines the sensitiv width of potential wells, whereas for potential barriers, the decay length of the matter wave in the region of the barrier qualifies the sensitive width of the barrier. The time evolution of the density profiles of the system during the reflection process is studied to disclose the different behaviors of matter waves in the region of the potential variation.</jats:p>

<jats:p>Quantum coherence and discord are two kinds of manifestations of nonclassicality. By calculating the coherence and discord in the specific bipartite quantum systems, we show quantitative connections between the coherence and the discord in the bipartite quantum systems created from local systems with the help of incoherent operations. We show that the coherence bounds the dynamical discord, and under particular conditions of the initial quantum states, the coherence of single systems is equal to the dynamical discord. We extend these results to the multipartite quantum systems.</jats:p>

<jats:p>LIGO-Virgo has observed the gravitational waves (GWs) from the coalescence of binary black hole (BBH) and binary neutron star (BNS) during O1 and O2, and the ones from NS-BH are expected to be hunted in the operating O3 run. The population properties and mass distribution of NS-BH mergers are poorly understood now, thus researchers simulated their chirp mass (<jats:inline-formula> <jats:tex-math> <?CDATA $ {\mathcal M} $?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>ℳ</mml:mi> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_30_12_120401_ieqn1.gif" xlink:type="simple" /> </jats:inline-formula>) distribution by a synthetic model, in which the BHs and NSs were inferred by LIGO-Virgo (O1/O2), and obtained the values in the range of <jats:inline-formula> <jats:tex-math> <?CDATA $2.1{M}_{\odot }\lt {\mathcal M} \lt 7.3{M}_{\odot }$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>2.1</mml:mn> <mml:msub> <mml:mi>M</mml:mi> <mml:mo>⊙</mml:mo> </mml:msub> <mml:mo>&lt;</mml:mo> <mml:mi>ℳ</mml:mi> <mml:mo>&lt;</mml:mo> <mml:mn>7.3</mml:mn> <mml:msub> <mml:mi>M</mml:mi> <mml:mo>⊙</mml:mo> </mml:msub> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_30_12_120401_ieqn2.gif" xlink:type="simple" /> </jats:inline-formula>. In this paper, we further simulate the GW frequency (<jats:italic>f</jats:italic> <jats:sub>GW</jats:sub>) distribution of NS-BH mergers by the above-stated synthetic model, with a basic binary system model through the Monte Carlo method. Our results predict that the median with 90% credible intervals is <jats:inline-formula> <jats:tex-math> <?CDATA ${165}_{-64}^{+475}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mrow> <mml:mn>165</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>64</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>475</mml:mn> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_30_12_120401_ieqn3.gif" xlink:type="simple" /> </jats:inline-formula> Hz in the case of Schwarzschild BH when the system just before merger, and this GW frequency is expected to increase several times in the merger stage, which is lying in the frequency band of LIGO-Virgo, i.e., about 15 Hz to a few kHz. Our results provide an important reference for hunting the NS-BH mergers by the on-going O3 run of LIGO-Virgo.</jats:p>

<jats:p>We numerically study the interaction dynamics of two bright solitons with zero initial velocities in the one-dimensional dipolar Bose–Einstein condensates. Under different dipolar strengths, the two bright solitons can merge into a breathing wave, and then split or propagate constantly after several oscillating periods. We quantitatively study the breathing frequency of wave after merging and the asymmetry property of solitons after splitting,and analyze their formation mechanism by the system’s energy evolution. Also, the change of initial phase difference brings distinct effects on the soliton interaction. Our results provide insight into the new dynamical phenomena in dipolar systems and enrich the understanding for interaction between dipolar solitons.</jats:p>

<jats:p>An improved heterogeneous dual memristive circuit (DMC) is proposed based on Chua’s circuit, which shows good symmetry and multistablility. For the difficulty in controlling the initial conditions, which restricts the engineering applications, the 3rd-order model (3OM) in flux–charge domain is derived from the 5th-order model (5OM) in volt–ampere domain by using the flux–charge analysis method (FCAM). The consistence of symmetry and multistability before and after dimensionality decreasing is meticulously investigated via bifurcation diagram, Lyapunov exponents, and especially attraction basins. The comparative analysis validates the effectiveness of reduction model and improves the controllability of the circuit. To avoid the noise in the analog circuit, a field-programmable gate array (FPGA) is utilized to realize the reduction model, which is rarely reported and valuable for relevant research and application.</jats:p>

<jats:p>This paper is concerned with the adaptive synchronization of fractional-order complex-valued chaotic neural networks (FOCVCNNs) with time-delay. The chaotic behaviors of a class of fractional-order complex-valued neural network are investigated. Meanwhile, based on the complex-valued inequalities of fractional-order derivatives and the stability theory of fractional-order complex-valued systems, a new adaptive controller and new complex-valued update laws are proposed to construct a synchronization control model for fractional-order complex-valued chaotic neural networks. Finally, the numerical simulation results are presented to illustrate the effectiveness of the developed synchronization scheme.</jats:p>

<jats:p>A new five-dimensional fractional-order laser chaotic system (FOLCS) is constructed by incorporating complex variables and fractional calculus into a Lorentz–Haken-type laser system. Dynamical behavior of the system, circuit realization and application in pseudorandom number generators are studied. Many types of multi-stable states are discovered in the system. Interestingly, there are two types of state transition phenomena in the system, one is the chaotic state degenerates to a periodical state, and the other is the intermittent chaotic oscillation. In addition, the complexity of the system when two parameters change simultaneously is measured by the spectral entropy algorithm. Moreover, a digital circuit is design and the chaotic oscillation behaviors of the system are verified on this circuit. Finally, a pseudo-random sequence generator is designed using the FOLCS, and the statistical characteristics of the generated pseudo-random sequence are tested with the NIST-800-22. This study enriches the research on the dynamics and applications of FOLCS.</jats:p>

<jats:p>Explosive synchronization (ES) is a first-order transition phenomenon that is ubiquitous in various physical and biological systems. In recent years, researchers have focused on explosive synchronization in a single-layer network, but few in multi-layer networks. This paper proposes a frequency-weighted Kuramoto model in multi-layer complex networks with star connection between layers and analyzes the factors affecting the backward critical coupling strength by both theoretical analysis and numerical validation. Our results show that the backward critical coupling strength of each layer network is influenced by the inter-layer interaction strength and the average degree. The number of network layers, the number of nodes, and the network topology can not directly affect the synchronization of the network. Enhancing the inter-layer interaction strength can prevent the emergence of explosive synchronization and increasing the average degree can promote the generation of explosive synchronization.</jats:p>

<jats:p>An extended car-following model with multiple delays is constructed to describe driver’s driving behavior. Through stability analysis, the stability condition of this uncontrolled model is given. To dampen the negative impact of the driver’s multiple delays (i.e., stability condition is not satisfied), a novel control strategy is proposed to assist the driver in adjusting vehicle operation. The control strategy consists of two parts: the design of control term as well as the design of the parameters in the term. Bifurcation analysis is performed to illustrate the necessity of the design of parameters in control terms. In the course of the design of parameters in the control term, we improve the definite integral stability method to reduce the iterations by incorporating the characteristics of bifurcation, which can determine the appropriate parameters in the control terms more quickly. Finally, in the case study, we validate the control strategy by utilizing measured data and configuring scenario, which is closer to the actual traffic. The results of validation show that the control strategy can effectively stabilize the unstable traffic flow caused by driver’s delays.</jats:p>

<jats:p>This paper addresses the distributed optimization problem of discrete-time multiagent systems with nonconvex control input constraints and switching topologies. We introduce a novel distributed optimization algorithm with a switching mechanism to guarantee that all agents eventually converge to an optimal solution point, while their control inputs are constrained in their own nonconvex region. It is worth noting that the mechanism is performed to tackle the coexistence of the nonconvex constraint operator and the optimization gradient term. Based on the dynamic transformation technique, the original nonlinear dynamic system is transformed into an equivalent one with a nonlinear error term. By utilizing the nonnegative matrix theory, it is shown that the optimization problem can be solved when the union of switching communication graphs is jointly strongly connected. Finally, a numerical simulation example is used to demonstrate the acquired theoretical results.</jats:p>