Abstracts:The present theoretical investigation covers a study of finding the multiple solutions of a Jeffery–Hamel flow and heat transfer under the influence of magnetic field. An analytical technique (Homotopy Analysis Method) is applied to solve the cylindrical form of governing equations after getting non-dimensional system using suitable transformation. It is noticed that dual solutions exist only for convergent channel case. Critical values of channel angle (αc ) are obtained which reveals the existence domain (αc  < α < 0) for multiple solutions in convergent channel flow. Stability analysis is also performed by constructing eigenvalue problem to predict the physically stable solution. The minimum positive eigenvalue justifies the fact that the growth of disturbances given to the solution decays with time. The effect of various pertinent physical parameters is shown graphically on velocity, temperature, skin friction coefficient and Nusselt number.

Abstracts:The issue of a recurrence of modulationally unstable water wave trains within the framework of the fully nonlinear potential Euler equations is addressed. It is examined, in particular, if a modulation, which appears from nowhere (i.e., is infinitesimal initially) and generates a rogue wave, can disappear with no trace. If so, this wave solution would be a breather solution of the primitive hydrodynamic equations. It is shown with the help of the fully nonlinear numerical simulation that when a rogue wave emerges from a uniform Stokes wave train, it excites other waves which have different lengths. This process prevents the complete recurrence and, eventually, results in a quasi-periodic breathing of the wave envelope. Meanwhile the discovered effects are rather small in magnitude, and the period of the modulation breathing may be thousands of the dominant wave periods. Thus, the obtained solution may be called a quasi-breather of the Euler equations.

Abstracts:Unknown signal recovery plays always a crucial role in the discipline of signal processing. Especially, a signal completely submerged by a strong noise is more difficult to be restored and identified in the engineering fields. Here, we provide an effective method to recognize the types and related parameters of an unknown signal in a strong noise background. Firstly, the nonlinear vibration approach is adopted to enhance an unknown weak signal with the assistance of proper noise, in which a new quantitative indicator is designed to keep the resonance response to follow the unknown signal features. Subsequently, the polynomial fitting and the variance of the time difference sequence are implemented to estimate several important signal parameters. Finally, the frequency spectrum of the recovered signal is compared with that of the original signal to verify the correctness of the restored signal. Recovery results of three typical signals indicate that the proposed method is effective. Moreover, unknown weak signals are obviously enhanced and signal features are completely preserved. The proposed method successfully takes advantage of the energy of the complex noise components. This work may pave the way for recovering unknown signal from a strong noise background.

Abstracts:Traveling wave solutions of a generalized KdV–Burgers equation are studied. The nonlinearity is specified as a piecewise linear flux function consisting of four parts. A boundary value shock-structure problem is solved. An analytical solution describing the structures of special discontinuities (undercompressive shocks) is obtained, and the behavior of these solutions is examined for various parameters of the problem.

Abstracts:Partnerships, between multiple sides that share cooperative goals, strive for mutual benefit, and acknowledge a high level of mutual interdependence, are ubiquitous both between and within the enterprises, and the internal or external stochastic factors driving competition and cooperation are the fundamental characteristics of partnership systems. Thus motivated, we establish an over-damped Langevin equation to describe the stochastic dynamical behaviors of the enterprise subject to asymmetric bistable Cobb–Douglas utility (CDU) potential. Due to the contemporaneous presence of periodic capital-product switches and stochastic fluctuations of internal and external capital environment, the stationary response of partnership systems is driven by the combination of the two driving effects cooperatively cause the enterprise to switch between the two utility equilibriums, and produce the maximum of stochastic incentive effect in the statistical sense. Based on the two-state theory, we derive the analytical results of performance measurement, including output signal-to-noise ratio (SNR), stationary unit risk-return (URR) and the incentive risk, which are divided into two categories: systematic risk and bilateral risk. Finally, one true example are introduced, and our proposed model is used to fitly explain the ‘U’-shape phenomenon observed from small and medium-sized enterprise (SME) samples. The purpose in this paper is to develop a quantitative method and the associated prototype system try to answer the questions of how the venture capital incents the partners especially associated with partnership success, what roles the internal and external risks play respectively, and how to avoid risk resonance and create portfolio strategies of introducing venture capital and optimizing the portfolio risk.

Abstracts:This paper presents a novel stability criterion of the time-lag fractional-order gene regulation network system(FGRNs) for stability analysis by means of Jensen inequality, Wirtinger inequality, fractional-order Lyapunov method and integral mean value theorem. The two inequalities are often seen, applied to the stability analysis of integer-order gene regulation network system, but rarely to that the FGRNs. However, this paper extends the general form of the Lyapunov-krasovskii function to a new fractional expression form by applying the definition of Caputo fractional derivative to the FGRNs. From the fractional-order Lyapunov method, the integral mean value theorem and the two inequalities, the novel stability criterion are deduced. It is the integral mean value theorem that reduces the conservatism of the stability criteria. Experiments show that the proposed criterion can satisfy all fractional-order operators from 0 to 1. It can not only solve the stability problem of the constant time-lag FGRNs, but also that of the time-varying time-lag FGRNs. Consequently, the novel stability criterion has generality and universality, which has been verified by numerical simulations for its effectiveness and generality.

Abstracts:In order to better understand and utilize the quarantine control when encountering outbreaks of infectious diseases, this paper introduces a nonlinear SIQS epidemic model on complex networks. By using complex network theory and Lyapunov function method, we obtain its basic reproduction number and global stability of both disease-free equilibrium and endemic equilibrium. Moreover, we investigate the optimal quarantine control problem for reducing control cost. By applying the optimal control theory, we obtain existence and uniqueness of the optimal control and the model’s optimal solution. These results are verified by some numerical examples, and the influence of network structure on the optimal control is also studied.

Abstracts:Stochastic noises are introduced to a model of androgen deprivation therapy of prostate cancer to study the effects of noises on tumors dynamics under treatment. Besides global analysis of the deterministic model, threshold conditions between extinction and persistence in mean for the stochastic system are obtained where noises play an important role in persistence and extinction of tumor cells. Sufficient conditions for the existence of stationary distribution are established. Finally, numerical simulations are given to illustrate the optimal treatment strategy and show the influences of noises on the growth of resistance cells.

Abstracts:This paper discusses the stability, transition and control of displaced non-Keplerian orbits by the spacecraft using low-thrust propulsion. The two-body dynamical model developed in the polar coordinates is parameterized by the thrust pitch angle, and then two of the hyperbolic and elliptic equilibria are solved from it. The bounded motions near two equilibria are investigated by dynamical system techniques to find out all the stable and unstable periodic trajectories, and two scenarios of the resonant periodic trajectory are presented. Regardless of the thrust pitch angle, all the transit orbits are numerically demonstrated to be restricted inside the invariant manifolds of Lyapunov orbit near the hyperbolic equilibrium. Then the transit orbits can be distinguished from non-transit ones by the restriction of three-dimensional invariant manifolds projected onto the Poincaré section or position space. Based on the influence of thrust direction on the system topology, operating the thrust pitch angle is an effective tool to achieve the transfer within different types of KAM tori, or even transfer beyond the KAM tori.

Abstracts:Experimental time series often contain bad segments that arise from artifacts, changes in experimental conditions, or failures in recording equipment. Such segments are usually removed from the time series during the preprocessing stage that can alter the correlation or other properties of the signals. Aiming to reveal how the effects of data loss depend on the amount of missing data, we consider here different regimes of regular and chaotic dynamics with excluded segments. Using several data processing techniques, namely, the wavelet-transform modulus maxima (WTMM) approach, the detrended fluctuation analysis (DFA) and the multiresolution analysis based on the discrete wavelet-transform (DWT), we demonstrate essentially different effects of the missing data for positively correlated time series and anti-correlated signals. All the techniques show that positively correlated time series are significantly less sensitive to excluded segments and enable the characterization of the object’s properties even under the condition of an extreme data loss. We verify the ability of characterizing physiological systems using an example of the cerebrovascular dynamics based on time series with missing data. A weak sensitivity of the cerebral blood flow to data loss is an important issue for diagnostic-related studies.