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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.

The purpose of this paper is to study analytically and numerically the Soret effect on double diffusive natural convection induced in a horizontal Darcy porous layer subject to lateral heat and mass fluxes. The work focuses on the particular situation where the solutal to thermal buoyancy forces ratio, N, is related to the Soret parameter, S_P, by the relation. For this particular situation, the rest state is a solution of the problem. The analytical identification of the parallel flow bifurcations counts among the objectives of the study. The effect of the governing parameters on the fluid flow properties and heat and mass transfer characteristics is also examined.

Both the Darcy model and the Boussinesq approximation are used for the mathematical formulation of the problem. The geometry under study is a horizontal porous cavity filled with a binary fluid. The problem is solved analytically on the basis of the parallel flow approximation, valid in the case of a shallow cavity. The analytical results are validated numerically using a second‐order finite difference method.

The main finding is the absence of a supercritical bifurcation for this problem. More precisely, in the studied case, only the subcritical convection was found possible for the parallel flow structure and its threshold was determined analytically versus the governing parameters. It is also shown that the S_P‐Le plane can be divided into two parallel flow regions; in one region the flow is counterclockwise while it is clockwise in the other. At sufficiently large values of R_T, two solutions of ψ0, termed as “stable” and “unstable” and varying, respectively, as R_T^1/3 and R_T⁻¹ were obtained. The flows corresponding to these solutions are rotating in the same direction with different intensities. An analytical expression is established for the critical Rayleigh number which allows a control of the onset of motion in the system.

The thermodiffusion phenomenon in saturated porous geometries is of practical interest in several natural and technological processes such as the migration of moisture through air contained in fibrous insulations, food processing, contaminant transport in ground water, electrochemical processes, etc.

The study concerns the Soret effect within a system subject to outside mass flux. Only one type of bifurcation (subcritical bifurcation) was found possible for the parallel flow structure in the present configuration instead of two kinds of bifurcations (supercritical and subcritical).

The purpose of this paper is to develop growth models that depart from the conventional framework, in the sense that consumption decisions take into account previous periods' expectations about output fluctuations. Households will raise their propensity to consume in periods of expected expansion and they will lower it in phases of predictable recession. Such a framework allows discussion of how growth trends may be disturbed over time as the result of changes in consumer sentiment.

Endogenous growth models are generally designed to address long‐term trends of growth. They explain how the economy converges with or diverges from a balanced growth path and they characterize aggregate behavior, given the optimization problem faced by a representative agent that maximizes consumption utility. In such frameworks, only potential output matters and all decisions, by firms and households, are taken on the assumption that any expectations on the value of the output gap do not interfere with the agents' behavior. Introducing consumer sentiment, a conventional growth model is modified in order to understand how effective output eventually deviates from the balanced growth path.

The proposed framework allows one to introduce nonlinear dynamics into the model, making it feasible to obtain, for reasonable parameter values, endogenous fluctuations. These are triggered by a Neimark‐Sacker bifurcation.

By introducing consumer confidence or consumer sentiment, it is possible to integrate the evaluation of growth and cycles into a unified framework. It is possible to explain business cycles as the result of the consumers' reaction to the expected performance of the economic system.

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.

The purpose of this paper is to address the problem of control in a typical chaotic power system. Chaotic oscillations cannot only extremely endanger the stabilization of the power system but they can also not be controlled by adding the traditional controllers. So, the sliding mode control based on a fuzzy supervisor can sufficiently ensure perfect tracking and controlling in the presence of uncertainties. Closed-loop stability is proved using the Lyapunov stability theory. The simulation results show the effectiveness of the proposed method in damping chaotic oscillations of the power system, eliminating control signal chattering and also show less control effort in comparison with the methods considered in previous literatures.

The sliding mode control based on a fuzzy supervisor can sufficiently ensure perfect tracking and controlling in the presence of uncertainties. Closed-loop stability is proved using the Lyapunov stability theory.

Closed-loop stability is proved using the Lyapunov stability theory. The simulation results show the effectiveness of the proposed method in damping chaotic oscillations of power system, eliminating control signal chattering and also less control effort in comparison with the methods considered in previous literatures.

Main contributions of the paper are as follows: the chaotic behavior of power systems with two uncertainty parameters and tracking reference signal for the control of generator angle and the controller signal are discussed; designing sliding mode control based on a fuzzy supervisor in order to practically implement for the first time; while the generator speed is constant, the proposed controller will enable the power system to go in any desired trajectory for generator angle at first time; stability of the closed-loop sliding mode control based on the fuzzy supervisor system is proved using the Lyapunov stability theory; simulation of the proposed controller shows that the chattering is low control signal.

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.

It is often observed in practice that the essential behavior of mathematical models involving many variables can be captured by a much smaller model involving only a few variables. Further, the simpler model very often displays oscillatory behavior of some sort, especially when critical problem parameters are varied in certain ranges. This paper attempts to supply arguments from the theory of dynamical systems for why oscillatory behavior is so frequently observed and to show how such behavior emerges as a natural consequence of focusing attention upon so‐called “essential” variables in the process of model simplification. The relationship of model simplification and oscillatory behavior is shown to be inextricably intertwined with the problems of bifurcation and catastrophe in that the oscillations emerge when critical system parameters, i.e. those retained in the simple model, pass through critical regions. The importance of the simplification, oscillation and bifurcation pattern is demonstrated here by consideration of several examples from the environmental, economic and urban areas.

The purpose of the study is to obtain explicit formulas to determine the stability of periodic solutions to the new system and study the extent of the stability of those periodic solutions and the direction of bifurcated periodic solutions. More than that, the authors did a numerical simulation to confirm the results that the authors obtained and presented through numerical analysis are the periodic and stable solutions and when the system returns again to the state of out of control.

The authors studied local bifurcation and verified its occurrence after choosing the delay as a parameter of control in Zhou 2019’s dynamical system with delayed feedback control. The authors investigated the normal form theory and the center manifold theorem.

The occurrence of local Hopf bifurcations at the Zhou's system is verified. By using the normal form theory and the center manifold theorem, the authors obtain the explicit formulas for determining the stability and direction of bifurcated periodic solutions. The theoretical results obtained and the corresponding numerical simulations showed that the chaos phenomenon in the Zhou's system can be controlled using a method of time-delay auto-synchronization.

As the delay increases further, the numerical simulations show that the periodic solution disappears, and the chaos attractor appears again. The obtained results can also be applied to the control and anti-control of chaos phenomena of system (1). There are still abundant and complex dynamical behaviors, and the topological structure of the new system should be completely and thoroughly investigated and exploited.

This paper aims to analyze the effect of aspect ratio A and aspect velocity ratio a on the bifurcation occurrence phenomena in lid-driven cavity by using finite volume method (FVM) and multigrid acceleration. This study has been performed for certain pertinent parameters; a wide range of the Reynolds number values has been adopted, and aspect ratios ranging from 0.25 to 1 and various velocity ratios from 0.25 to 0.825 have been considered in this investigation. Results show that the transition to the unsteady regime follows the classical scheme of Hopf bifurcation, giving rise to a perfectly periodic state. Flow periodicity has been verified through time history plots for the velocity component and phase-space trajectories as a function of Reynolds number. Velocity profile for special case of a square cavity (A = 1) was found to be in good agreement between current numerical results and published ones. Flow characteristics inside the cavity have been presented and discussed in terms of streamlines and vorticity contours at a fixed Reynolds number (Re = 5,000) for various aspect ratios (a = 0).

The numerical method is based on the FVM and multigrid acceleration.

Computations have been investigated for several Reynolds numbers and aspect ratios A (0.25, 0.5, 0.75, 0.825 and 1). Besides, various velocity ratios (a = 0.25, 0.5, 0.75 and 0.825) at fixed aspect ratios (A = 0.25, 0.5 and 0.75) were considered. It is observed that the transition to the unsteady regime follows the classical scheme of Hopf bifurcation, giving rise to a perfectly periodic state. Flow periodicity is verified through time history plots for velocity components and phase-space trajectories.

The bifurcations between steady and unsteady states are investigated.