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On the ground of the Hopf bifurcation theory derived by Hassard et al., the purpose of this paper is to investigate the weakly nonlinear dynamics of transverse rough‐surface short journal bearings.

By application of the stochastic model of rough surfaces, developed by Christensen and Tonder, the roughness effects of transverse surface patterns on the bifurcation behaviors close to the Hopf bifurcation point are investigated.

It is found that the dynamic behavior of transverse rough‐surface short journal bearings can display Hopf bifurcation phenomena. Comparing with the case of isotropic rough‐surface bearing by Lin, under the same parameters, the effects of transverse surface roughness provide a reduced sub‐critical Hopf bifurcation region as well as an increased super‐critical Hopf bifurcation region. In addition, the effects of transverse surface roughness result in a lower stability‐threshold critical speed for both the sub‐critical bifurcation profile and the super‐critical bifurcation profile.

The present study, associated with the results of Hopf bifurcation regions and periodic orbits, can provide useful information for engineers when the transverse surface roughness effects and the bifurcation behavior are considered in a journal bearing system.

This study aims to research the prediction performance of the bifurcation approach with different base models in different kinds of turbulent flows with rotation and curvature.

The k−ω and Shear-Stress Transport (SST) k−ω models are modified by using the complete eddy viscosity coefficient expression, and the latter is modified by using two sets of model coefficients. The two bifurcation models were tested in three cases: rotating channel flow with system rotation, Taylor–Couette flow with wall rotation and curvature effect and swirling flow through an abrupt axisymmetric expansion with inlet swirling flow.

In these flows, the bifurcation approach can significantly improve the prediction performance of the base model in the fluctuation velocity. The deviation of the BSkO model is slightly superior to the BkO model by about 2% in the Taylor–Couette flow. The prediction effect of the root-mean-square (RMS) velocity of the BSkO model increases by about 4–5% as the number of grids increases about 2.37 times, and the best is the Large Eddy Simulation (LES) grid used. Finally, compared with the SST k−ω model, the average iteration time of the SST with curvature correction (SST-CC), bifurcation k−ω (BkO) and bifurcation SST k−ω (BSkO) models increased by 27.7%, 86.9% and 62.3%, respectively.

This study is helpful to understand further the application of the bifurcation method in the turbulence model.

The aim of this paper is to develop a new method for finding multiple bifurcation points in structures.

A brief review of nonlinear analysis is presented. A powerful method (called arc‐length) for tracing nonlinear equilibrium path is described. Techniques for monitoring critical points are discussed to find the rank deficiency of the stiffness matrix. Finally, by using eigenvalue perturbation of tangent stiffness matrix, load parameter associated with multiple bifurcation points is obtained.

Since other methods of finding simple bifurcation points diverge in the neighborhood of critical points, this paper introduces a new method to find multiple bifurcation points. It should be remembered that a simple bifurcation point is a multiple bifurcation point with rank deficiency equal to one. Therefore, the method is applicable to simple critical points as well.

Global buckling of the structures should be considered in design. Many structures (specially symmetric space structures) have multiple bifurcation points, therefore, analyst and designer should be aware of these points and should control them (for example, by changing the geometry or other related factors) for obtaining a safe and optimum design.

In this paper a robust method to find multiple bifurcation points is introduced. By using this method, engineers can be aware of critical load of multiple bifurcation points to control global buckling of related structures.

In general, the bifurcation phenomenon of the natural convection has largely been studied. But the bifurcation of natural convection under magnetic conditions has not been studied as per the authors’ knowledge. This paper aims to investigate the changes in bifurcation phenomenon by the self-induced circular magnetic field.

The authors numerically solved the natural convection in an annulus. The SIMPLE algorithm was adopted for pressure-momenturm coupling. The Boussinesq approximation was used for numerical modeling of natural convection. Finally, the Lorentz force effect by the magnetic field was considered through the source terms in the momentum conservation equation.

It was determined that the heat-transfer rate changes by 17% owing to the applied magnetic effect, and the range of the Rayleigh number for flow bifurcation is changed by the magnetic effect. Moreover, under the strong magnetic condition, the flow bifurcation continues even at very high Ra. Previously, flow bifurcation has been understood as a flow instability phenomena, and the Lorentz force was regarded as a flow-damping effect; however, in this study, it was found that the magnetic field can boost the flow instability and induce flow bifurcation even in the Rayleigh number region where the bifurcation does not appear.

This paper is dealing with the bifurcation phenomenon in MHD natural convection problems. In the past, the electromagnetic forces were regarded as always acting to damp out the existing flows; herewith, the authors first investigated that the magnetic effect can boost the bifurcation of a kind of flow instability phenomenon.

When a reflected shock interacts with the boundary layer in a shock tube, the shock bifurcation occurs near the walls. Although the study of the shock bifurcation has been carried out by many researchers for several decades, little attention has been devoted to investigate the instability pattern of the bifurcation. This research work aims to successfully capture the asymmetry of the whole flow field, and attempt to achieve the instability mechanism of the shock bifurcation by a direct numerical simulation of the reflected shock wave/boundary layer interaction at Ma = 1.9. In addition, the reason for the formation of the bifurcated structure is also explored.

The spatial and temporal evolution of the shock bifurcation is obtained by solving the two-dimensional compressible Navier–Stokes equations using a seventh-order accurate weighted essentially non-oscillatory (WENO) scheme and a three-step Runge–Kutta time advancing approach.

The results show that the formation of shock bifurcation is mainly because of the shock/gradient field interaction, and the height of the bifurcated foot increases with the growth of the shock intensity and the gradient field. The unsteady asymmetry of the upper and bottom shock bifurcated structures is because of the vortex shedding with high frequency in the rear recirculation zone, which leads to the fluctuation of the recirculation area. The vortex shedding process behind the bifurcated structure closely resembles the Karman vortex street formed by the flow around the cylinder. The dimensionless vortex shedding frequency varies between 0.01 and 0.02. In comparison to the scenario at Ma = 1.9, the occurring time of instability is delayed and the upper and bottom bifurcated feet intersect in a relatively short time at Ma = 3.5. The region behind the bifurcated shock is a transitional flow field containing obvious cell structures and “isolated islands.”

This paper discovers an unsteady flow pattern of the shock bifurcation, and the mechanism of this instability in the reflected shock/boundary layer interaction is revealed in detail.

Possible asymmetric treatment among family members has long been neglected in the field of family firm research. To fill this gap, the purpose of this study is to shed light on the heterogeneity of treatment of family members in family firms by proposing factors that influence the likelihood of bifurcation bias among “family” members.

Drawing upon social identity theory and the concept of bifurcation bias, the authors theorize that family members working in family firms are not a homogenous entity, but rather a heterogeneous entity contingent on their status and/or position in the family. To provide a comprehensive understanding of heterogeneous treatment among family members, both individual factors and societal factors should be considered.

Blood relatedness of family members is suggested as an important determinant of the likelihood of bifurcation bias among family members. It is also proposed that the impact of blood relatedness is likely influenced by both individual factors (familial proximity and familial tenure) and a societal factor (collectivism).

Theorizing takes a step forward to advance the understanding of interpersonal dynamics in family firms. In particular, this article expands the research boundaries of family business research by taking into account that not all “family” members are treated preferentially. Moreover, this article deepens our understanding of the nature and status of non-blood related family members by unveiling the influence of both individual and societal factors. This article also provides a theoretical foundation for human resource management (HRM) research in family businesses by addressing bifurcation bias among family members.

Cascaded DC-DC converters system is the main structure of distributed power system, and it has complex nonlinear phenomena during operation, which affect the power quality. Therefore, the dynamic behavior of the cascaded buck converter and boost converter system, as one of the typical cascaded DC-DC converters systems is analyzed.

Firstly, the studied cascaded system of the buck converter with peak current control and the boost converter with PI current control is introduced and its discrete modeling is built. Then, the Jacobian matrix of the cascaded system is calculated to research the stability when the parameter change. Finally, simulation by PSIM and experiments are carried out to verify the theoretical analysis.

The coexistence of fast and slow time scale bifurcations with the changes of reference current and input voltage are studied in the cascaded system, and using simulation analysis to further study the sensitivity of the inductor current of the front-stage converter and back-stage converter to different parameters.

A discrete model of the cascaded buck converter and boost converter system is established, and its dynamic behavior is analyzed in detail for the first time.

This paper aims to investigate the singular Hopf bifurcation and mixed mode oscillations (MMOs) in the perturbed Bonhoeffer-van der Pol (BVP) circuit. There is a singular periodic orbit constructed by the switching between the stable focus and large amplitude relaxation cycles. Using a generalized fast/slow analysis, the authors show the generation mechanism of two distinct kinds of MMOs.

The parametric modulation can be used to generate complicated dynamics. The BVP circuit is constructed as an example for second-order differential equation with periodic perturbation. Then the authors draw the bifurcation parameter diagram in terms of a containing two attractive regions, i.e. the stable relaxation cycle and the stable focus. The transition mechanism and characteristic features are investigated intensively by one-fast/two-slow analysis combined with bifurcation theory.

Periodic perturbation can suppress nonlinear circuit dynamic to a singular periodic orbit. The combination of these small oscillations with the large amplitude oscillations that occur due to canard cycles yields such MMOs. The results connect the theory of the singular Hopf bifurcation enabling easier calculations of where the oscillations occur.

By treating the perturbation as the second slow variable, the authors obtain that the MMOs are due to the canards in a supercritical case or in a subcritical case. This study can reveal the transition mechanism for multi-time scale characteristics in perturbed circuit. The information gained from such results can be extended to periodically perturbed circuits.