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This paper investigates the streamline topologies and stability of stagnation points and their bifurcations for an asymmetric peristaltic flow. The asymmetry of channel is due to the propagation of peristaltic waves with different phases and amplitudes on the flexible channel walls. An exact analytic solution of the flow problem subject to the constraints of low Reynolds number and long wavelength is obtained in wave frame of reference moving with wave velocity. A system of nonlinear differential equations is established to locate and classify the stagnation points in the flow domain. Different flow situations, manifested in the flow field, are categorized as: backward flow, trapping, and augmented flow. The transition from one situation to the other corresponds to bifurcation, which is explored graphically through local and global bifurcation diagrams. This analysis discloses the stability status of stagnation points and ranges of involved parameters in which various flow conditions appear in the flow field. It is concluded that the trapping in an asymmetric peristaltic transport can be reduced by increasing the phase difference of the channel walls. It is also found that the augmented flow region shrinks and the trapping region expands by increasing the amplitude ratio of the channel walls. Key words: peristaltic flow, asymmetric channel, streamline topologies, non-linear dynamical system, bifurcation. Nous examinons ici les topologies des lignes de courant, la stabilite des points de stagnation et leurs bifurcations dans un ecoulement peristaltique asymetrique. L'asymetrie du canal est due a la propagation d'ondes peristaltiques avec differentes phases et amplitudes sur la surface flexible des murs du canal. Nous obtenons, dans le referentiel de l'onde se deplacant avec la vitesse de l'onde, une solution analytique exacte du probleme de flot sujet aux contraintes de faible nombre de Reynolds et de grande longueur d'onde. Nous developpons un systeme d'equations differentielles non lineaires pour localiser et classifier les points de stagnation dans le champ d'ecoulement. Differentes situations de flot se manifestant dans le flot sont categorisees comme : flot de recul, de piegeage et augmente. La transition d'une situation a une autre correspond a une bifurcation qui est examinee graphiquement a l'aide de diagrammes de bifurcation locaux et globaux. Cette analyse nous indique le statut de stabilite des points de stagnation et les domaines des parametres impliques pour lesquels differentes conditions de flot apparaissent dans le champ d'ecoulement. Nous en concluons que le piegeage dans un transport peristaltique asymetrique peut etre reduit en augmentant la difference de phase des murs du canal. Nous trouvons egalement que la region de flot augmente diminue et que la region de piegeage croit en augmentant le rapport d'amplitude entre les murs du canal. [Traduit par la Redaction] Mots-cles : ecoulement-flot peristaltique, canal asymetriquem, topologies des lignes de courant, systeme dynamique non lineaire, bifurcation., 1. Introduction The phenomenon in which a wave of contraction-relaxation transmitted to the conduit wall affects the movement of enclosed material is referred to as peristaltic transport. Extensive research on [...]

We answer to a problem raised by recent work of Jelonek and Kurdyka: how can one detect by rational arcs the bifurcation locus of a polynomial map [Formula omitted] in case [Formula omitted]. We describe an effective estimation of the 'non-trivial' part of the bifurcation locus., Author(s): Luis Renato G. Dias [sup.1] , Susumu Tanabé [sup.2] , Mihai Tibar [sup.3] Author Affiliations: (1) 0000 0004 4647 6936grid.411284.aFaculdade de Matemática, Universidade Federal de Uberlândia, Av. João Naves [...]

We study the structure of the solution set of a class of infinite-horizon dynamic programming problems with one- dimensional state spaces, as well as their bifurcations, as problem parameters are [...]

Bifurcations throughout the vascular system are among the most common locations that atherosclerosis may form. Within the span of an arterial bifurcation, uniform flow is disrupted and more complex mechanical situations exist. Analysis of a flow path complicated by a change in direction is much more complex than studying flow patterns through a single channel. For this purpose, modeling an arterial bifurcation with sylgard 184 may allow for extensive analysis of the system. Therefore, the purpose of this study is to develop a rapid and inexpensive method to develop consistent bifurcation models. In order to model an arterial bifurcation with precise dimensions, a two-stage mold design has been strategized. The initial mold is injected with a material to form the inner cast, which is then placed into the secondary mold. Sylgard is injected into the secondary mold to cover the inner cast. Once the sylgard cures, the coated inner cast is removed from the secondary mold and then melted out of the sylgard, leaving a bifurcation shaped tube behind. Three types of materials, molding wax, polymers, and low-temp melting metals, were tested as the inner mold. Results demonstrated that the low-temp melting metal possesses the best properties for our application. Upcoming challenges will focus on the injection procedures and the manufacture of the mold. With a repeatable process for modeling bifurcations, these studies will potentially lead to more accurate testing of cardiovascular devices, such as stents, in a laboratory setting., INTRODUCTION Atherosclerosis and hypertension are the most common causes of cardiovascular disease. Atherosclerosis is the thickening of a vessel wall due to absorption of fatty materials such as cholesterol and [...]

During the decline to extinction, animal populations may present dynamical phenomena not exhibited by robust populations (1,2). Some of these phenomena, such as the scaling of demographic variance, are related to small size (3-6) whereas others result from density-dependent nonlinearities (7). Although understanding the causes of population extinction has been a central problem in theoretical biology for decades (8), the ability to anticipate extinction has remained elusive (9). Here we argue that the causes of a population's decline are central to the predictability of its extinction. Specifically, environmental degradation may cause a tipping point in population dynamics, corresponding to a bifurcation in the underlying population growth equations, beyond which decline to extinction is almost certain. In such cases, imminent extinction will be signalled by critical slowing down (CSD). We conducted an experiment with replicate laboratory populations of Daphnia magnato test this hypothesis. We show that populations crossing a transcritical bifurcation, experimentally induced by the controlled decline in environmental conditions, show statistical signatures of CSD after the onset of environmental deterioration and before the critical transition. Populations in constant environments did not have these patterns. Four statistical indicators all showed evidence of the approaching bifurcation as early as 110 days (~8 generations) before the transition occurred. Two composite indices improved predictability, and comparative analysis showed that early warning signals based solely on observations in deteriorating environments without reference populations for standardization were hampered by the presence of transient dynamics before the onset of deterioration, pointing to the importance of reliable baseline data before environmental deterioration begins. The universality of bifurcations in models of population dynamics suggests that this phenomenon should be general (10-12)., At present, habitat destruction and degradation are the major threats to viability for the majority of globally threatened or endangered bird (1,045), amphibian (1,641) and mammal (≥ 652) species (13). [...]

In methanogenic Archaea, the final step of methanogenesis generates methane and a heterodisulfide of coenzyme M and coenzyme B (CoM-S-S-CoB). Reduction of this heterodisulfide by heterodisulfide reductase to regenerate HS-CoM and HS-CoB is an exergonic process. Thauer et al. [Thauer, et al. 2008 Nat Rev Microbiol 6:579-591] recently suggested that in hydrogenotrophic methanogens the energy of heterodisulfide reduction powers the most endergonic reaction in the pathway, catalyzed by the formylmethanofuran dehydrogenase, via flavin-based electron bifurcation. Here we present evidence that these two steps in methanogenesis are physically linked. We identify a protein complex from the hydrogenotrophic methanogen, Methanococcus maripaludis, that contains heterodisulfide reductase, formylmethanofuran dehydrogenase, [F.sub.420]-nonreducing hydrogenase, and formate dehydrogenase. In addition to establishing a physical basis for the electronbifurcation model of energy conservation, the composition of the complex also suggests that either [H.sub.2] or formate (two alternative electron donors for methanogenesis) can donate electrons to the heterodisulfide-[H.sub.2] via [F.sub.420]-nonreducing hydrogenase or formate via formate dehydrogenase. Electron flow from formate to the heteroclisulfide rather than the use of [H.sub.2] as an intermediate represents a previously unknown path of electron flow in methanogenesis. We further tested whether this path occurs by constructing a mutant lacking [F.sub.420]-nonreducing hydrogenase. The mutant displayed growth equal to wild-type with formate but markedly slower growth with hydrogen. The results support the model of electron bifurcation and suggest that formate, like [H.sub.2], is closely integrated into the methanogenic pathway. energy conservation | Archaea | formate dehydrogenase | forrnylrnethanofuran dehydrogenase | [F.sub.420]-nonreducing hydrogenase doi/ 10.1073/pnas.1003653107

A numerical method is introduced for the computation of time-periodic vortex sheets with surface tension separating two immiscible, irrotational, two-dimensional ideal fluids of equal density. The approach is based on minimizing a nonlinear functional of the initial conditions and supposed period that is positive unless the solution is periodic, in which case it is zero. An adjoint-based optimal control technique is used to efficiently compute the gradient of this functional. Special care is required to handle singular integrals in the adjoint formulation. Starting with a solution of the linearized problem about the flat rest state, a family of smooth, symmetric breathers is found that, at quarter-period time intervals, alternately pass through a flat state of maximal kinetic energy, and a rest state in which all the energy is stored as potential energy in the interface. In some cases, the interface overturns before returning to the initial, flat configuration. It is found that the bifurcation diagram describing these solutions contains several disjoint curves separated by near-bifurcation events. adjoint method | bifurcation | fluid interface | optimal control | standing waves doi/10.1073/pnas.09010830107

Recent research on braided river morphology shows that the intensity (number of anabranches) of braiding channels increases with dimensionless discharge and (or) stream power. This variation in intensity reflects the adjustment of total sinuosity of the river to imposed gradient at a given discharge and grain size. Only a subset of channels is active at a given time and this active braiding intensity reflects the limited number of channels that can sustain bed load transport as the flow is divided. This is governed mechanistically by the dynamics of bifurcations and avulsions. Braided channel networks also have a characteristic length scale (or scales) related to the wavelength of the bars from which braiding develops and to the scale of the bars and confluence-bifurcation units within the braided network. The range of scales is limited by the size (and, therefore, number) of the active channels within the network and the width of the entire river. Key words: river regime, braiding, fluvial geomorphology, river mechanics, sediment transport, bars, bifurcation, channel pattern. Les recherches recentes sur la morphologie des rivieres anastomosees montrent que l'intensite (le nombre de bras de la riviere anastomosee) des petits chenaux entrelaces augmente avec la decharge adimensionnelle et/ou la force du ruisseau. Cette variation d'intensite reflete l'ajustement de la sinuosite totale de la riviere a un gradient impose pour une decharge et une granulometrie donnees. Seul un sous-ensemble de canaux est actif a tout moment donne et cette intensite de chenaux entrelaces actifs reflete le nombre limite de canaux qui peuvent soutenir le transport de la charge de fond lorsque l'ecoulement est divise. Ce nombre limite est regi de maniere mecaniste par la dynamique des embranchements et des avulsions. Les reseaux de canaux anastomoses possedent aussi une ou plusieurs echelles de longueur caracteristiques reliees a la longueur d'onde des barres a partir desquelles se developpe le reseau anastomose ainsi qu'a l'echelle des barres et au nombre de confluences-embranchements dans le reseau de canaux anastomoses. La plage d'echelles est limitee par la dimension (et, donc, le nombre) des canaux actifs dans le reseau et par la largeur entiere de la riviere. Mots-cles: regime d'ecoulement, developpement d'un reseau anastomose, geomorphologie fluviale, mecanique des rivieres, transport de sediments, barres, embranchements, forme de canaux. [Traduit par la Redaction], 1. Introduction Braided rivers are a distinctive alluvial river morphology characterized by multiple intersecting channels separated by ephemeral (and usually unvegetated) exposed bars (Fig. 1). Braiding is a 'self-induced form' [...]

Data from the genome sequence of the aerobic, marine bacterium Roseovarius nubinhibens ISM were interpreted such that 3-sulfolactate would be degraded as a sole source of carbon and energy for growth via a novel bifurcated pathway including two known desulfonative enzymes, sulfoacetaldehyde acetyltransferase (EC 2.3.3.15) (Xsc) and cysteate sulfo-lyase (EC 4.4.1.25) (CuyA). Strain ISM utilized sulfolactate quantitatively with stoichiometric excretion of the sulfonate sulfur as sulfate. A combination of enzyme assays, analytical chemistry, enzyme purification, peptide mass fingerprinting, and reverse transcription-PCR data supported the presence of an inducible, tripartite sulfolactate uptake system (SIcHFG), and a membrane-bound sulfolactate dehydrogenase (SlcD) which generated 3-sulfopyruvate, the point of bifurcation. 3-Sulfopyruvate was in part decarboxylated by 3-sulfopyruvate decarboxylase (EC 4.1.1.79) (ComDE), which was purified. The sulfoacetaldehyde that was formed was desulfonated by Xsc, which was identified, and the acetyl phosphate was converted to acetyl-coenzyme A by phosphate acetyltransferase (Pta). The other portion of the 3-sulfopyruvate was transaminated to (S)-cysteate, which was desulfonated by CuyA, which was identified. The sulfite that was formed was presumably exported by CuyZ (TC 9.B.7.1.1 in the transport classification system), and a periplasmic sulfite dehydrogenase is presumed. Bioinformatic analyses indicated that transporter SlcHFG is rare but that SlcD is involved in three different combinations of pathways, the bifurcated pathway shown here, via CuyA alone, and via Xsc alone. This novel pathway involves ComDE in biodegradation, whereas it was discovered in the biosynthesis of coenzyme M. The different pathways of desulfonation of sulfolactate presumably represent final steps in the biodegradation of sulfoquinovose (and exudates derived from it) in marine and aquatic environments.

This paper presents the stability analysis for a distribution static compensator (DSTATCOM) that operates in current control mode based on bifurcation theory. Bifurcations delimit the operating zones of nonlinear circuits and, hence, the capability to compute these bifurcations is of important interest for practical design. A control design for the DSTATCOM is proposed. Along with this control, a suitable mathematical representation of the DSTATCOM is proposed to carry out the bifurcation analysis efficiently. The stability regions in the Thevenin equivalent plane are computed for different power factors at the point of common coupling. In addition, the stability regions in the control gain space, as well as the contour lines for different Floquet multipliers are computed. It is demonstrated through bifurcation analysis that the loss of stability in the DSTATCOM is due to the emergence of a Neimark bifurcation. The observations are verified through simulation studies. Index Terms--Distribution static compensator (DSTATCOM), floquet multiplier, Neimark bifurcation, point of common coupling (PCC), stability regions.

A unique T-beam microresonator designed to operate on the principle of nonlinear modal interactions due to 1 : 2 internal resonance is introduced. Specifically, the T-structure is designed to have two flexural modes with natural frequencies in a 1:2 ratio, and the higher frequency mode autoparametrically excites the lower frequency mode through inertial quadratic nonlinearities. A Lagrangian formulation is used to model the electrostatically actuated T-beam resonator, and it includes inertial quadratic nonlinearities, cubic nonlinearities due to midplane stretching and curvature of the beam, electrostatic potential, and effects of thermal prestress. A nonlinear two-mode reduced-order model is derived using linear structural modes in desired internal resonance. The model is used to estimate static pull-in bias voltages and dynamic responses using asymptotic averaging. Nonlinear frequency responses are developed for the case of resonant actuation of a higher frequency mode. It is shown that the lower frequency flexural mode is excited for actuation levels above a certain threshold and generates response component at half the frequency of resonant actuation. The effects of damping, thermal prestress, and mass and geometric perturbations from nominal design are thoroughly discussed. Finally, experimental results for a macroscale T-beam structure are briefly described and qualitatively confirm the basic analytical predictions. The T-beam resonator shows a high sensitivity to mass perturbations and, thus, holds great potential as a radio frequency filter-mixer and mass sensor. [2008-0107] Index Terms--Bifurcation, microresonators, nonlinear oscillators, reduced-order systems, resonator filters.

In this paper, the chaotic characteristic of the Sprott N system with parameter is studied in theoretical analysis and numerical simulations, and abundant dynamical behavior is presented. When the parameter β = 1.9, the system exist chaotic attractor. The abundance dynamical behavior of the system is presented by the global bifurcation graph and the Lyapunov exponent. In order to realize the full state hybrid projective synchronization (FSHPS) of the system, Smarandache controller is design. Numerical simulations show that the controller works well. Keywords Chaos, Bifurcation, The Sprott N system with parameter, FSHPS., §1. Introduction Since synchronization of chaotic systems was first introduced by Fujisaka and Yamada [1] and Pecora and Carroll [2]. Due to the importance and applications of coupled systems, ranging [...]

We present a model to explain how the neurosecretory system of aquatic mollusks generates their diversity of shell structures and pigmentation patterns. The anatomical and physiological basis of this model sets it apart from other models used to explain shape and pattern. The model reproduces most known shell shapes and patterns and accurately predicts how the pattern alters in response to environmental disruption and subsequent repair. Finally, we connect the model to a larger class of neural models. neurosecretory | mathematical model | bifurcation

Plasma channel generation (or filamentation) using ultraintense laser pulses in dielectric media has a wide spectrum of applications, ranging from remote sensing to terahertz generation to lightning control So far, laser filamentation has been triggered with the use of ultrafast pulses with axially symmetric spatial beam profiles, thereby generating straight filaments. We report the experimental observation of curved plasma charmers generated in air using femtosecond Airy beams. In this unusual propagation regime, the tightly confined main intensity feature of the axially nonsymmetric laser beam propagates along a bent trajectory, leaving a curved plasma channel behind. Secondary channels bifurcate from the primary bent channel at several locations along the beam path. The broadband radiation emanating from different longitudinal sections of the curved filament propagates along angularly resolved trajectories.

Using a high-performance polycrystalline-silicon micromachined actuator that also functions as a friction tester, we have found frictional forces that cannot be explained by Amontons' law with a constant coefficient of friction. In our friction test, a constant tangential force is applied while normal load is ramped down at a rate [F.sub.n] after a hold time [t.sub.h] at a hold load [F.sub.h]. When coated by a monolayer of FOTAS ([CF.sub.3][C.sub.5][F.sub.10][C.sub.2][H.sub.4] Si([N([C[H.sub.3]).sub.2]).sub.3]), we find that there is no unique coefficient of static friction [[micro].sub.s], but instead that [[micro].sub.s] depends on all three of these parameters. The dependence on [t.sub.h] implies static friction aging, but the rate of static friction aging can be suppressed by greater hold force. When sliding motion begins, we have identified a critical normal force to shear force ratio such that any motion initiating above the critical ratio proceeds with time-dependent frictional creep over several hundred nanometers, whereas any motion initiating below the critical ratio proceeds with a large inertial jump. These effects demonstrate that contact aging effects extend from the micrometer to the nanometer scale and are relevant to micromachined interfaces. [2008-0174] Index Terms--Actuators, friction, stepper motors.

A novel current mode control scheme for the tristate boost converter circuit is proposed, which eliminates the zero in the right-half plane (RHP), and improves the dynamic performance. The tristate boost converter contains an additional switch across the inductor. Within a clock cycle, the inductor current first rises during the ON interval of the main switch, then falls during the OFF or capacitor charging interval, and finally, remains almost constant during the freewheeling interval when the additional switch is turned on. In the proposed controller, the peak value of the inductor current is controlled by peak current mode control using an outer voltage feedback loop, whereas the freewheeling current is controlled by the input voltage and the reference voltage feedforward path. Applying both feedback as well as feedforward control on the inductor current significantly improves the output voltage regulation, audio susceptibility, and transient responses. We show that the RHP zero is completely eliminated from the closed-loop control-to-output transfer function. This results in a very large bandwidth, and hence a superior dynamic performance. The latter is established by comparison with the voltage-mode- and current-mode-controlled classical boost converters that suffer from the RHP zero problem, as well as with other tristate boost converter control techniques like the constant charging interval and dual mode control, recently proposed in the literature. Significant superiority of the proposed scheme is established both through simulation and experimentation. Index Terms--Bifurcation, dc-dc power conversion, feedback systems, feedforward systems, pulsewidth modulated power converters, stability criteria, switching circuits, transient response.

In light of the rapid recent retreat of Arctic sea ice, a number of studies have discussed the possibility of a critical threshold (or 'tipping point') beyond which the ice--albedo feedback causes the ice cover to melt away in an irreversible process. The focus has typically been centered on the annual minimum (September) ice cover, which is often seen as particularly susceptible to destabilization by the ice--albedo feedback. Here, we examine the central physical processes associated with the transition from ice-covered to ice-free Arctic Ocean conditions. We show that although the ice--albedo feedback promotes the existence of multiple ice-cover states, the stabilizing thermodynamic effects of sea ice mitigate this when the Arctic Ocean is ice covered during a sufficiently large fraction of the year. These results suggest that critical threshold behavior is unlikely during the approach from current perennial sea-ice conditions to seasonally ice-free conditions. In a further warmed climate, however, we find that a critical threshold associated with the sudden loss of the remaining wintertime-only sea ice cover may be likely. Arctic climate | bifurcation | climate change | tipping point

Local robust analysis via [[laplace].sub.2] gain method is presented for a class of Hopf bifurcation stabilizing controllers. In particular, we first construct a family of Lyapunov functions for the corresponding critical system, then derive a sufficient condition to compute the [[laplace].sub.2] gain by solving the Hamilton-Jacobi-Bellman (HJB) inequalities. Local robust analysis can be conducted through computing the local [[laplace].sub.2] gain achieved by the stabilizing controllers at the critical situation. The theoretical results obtained in this brief provide useful guidance for selecting a robust controller from a given class of stabilizing controllers under Hopf bifurcation. As an example, application to a modified Van der Pol oscillator is discussed in details. Index Terms--Bifurcation stabilization, Hopf bifurcation, robustness, Van der Pol oscillators, [[laplace].sub.2] gain.

Synchronization is deemed to play an important role in information processing in many neuronal systems. In this work, using a well known technique due to Pecora and Carroll, we investigate the existence of a synchronous state and the bifurcation diagram of a network of synaptically coupled neurons described by the Hindmarsh-Rose model. Through the analysis of the bifurcation diagram, the different dynamics of the possible synchronous states are evidenced. Furthermore, the influence of the topology on the synchronization properties of the network is shown through an example. Index Terms--Bifurcation, biological systems, networks, nonlinear oscillators, synchronization.

DC-DC converters have been reported as exhibiting a wide range of bifurcations and chaos under certain conditions. This paper analyzes the bifurcations in current-controlled Luo topology operating in continuous conduction mode using continuous-time model. The stability of the system is analyzed by studying the locus of the complex eigenvalues, and the characteristic multipliers locate the onset of Hopf bifurcation. The 1-periodic orbit loses its stability via Hopf bifurcation, and the resulting attractor is a quasi-periodic orbit. This later bifurcates to chaos via border collision bifurcation. A computer simulation using MATLAB/SIMULINK confirms the predicted bifurcations. It has also been inferred from the experimental results that the margin of system stability decreases as the load decreases. Index Terms--Border collision bifurcation, continuous-time model, Hopf bifurcation, Luo converter.

This paper investigates the coexisting fast-scale and slow-scale bifurcations in simple dc/dc converters under peak current-mode control operating in continuous conduction mode. Our focus is the boost converter as it is a representative form of dc/dc converter requiring current-mode control. Effects of varying the input voltage and some chosen parameters on the qualitative behavior of the system are studied in detail. Analysis based on a nonlinear simplified discrete-time model, which takes into account the effects of parasitics, is performed to investigate the coexistence of fast-scale and slow-scale bifurcations, and to identify the different types of bifurcation. Boundaries of stable region, slow-scale bifurcation region, fast-scale bifurcation region, coexisting fast and slow-scale bifurcation region are identified. Experimental measurements of the boost converter are provided for verification of the analytical results. Index Terms--Bifurcation, current-mode control, dc/dc converters, fast-scale instability, slow-scale instability.

In this study, a two-stage simulation method is presented for the efficient design of frequency dividers using harmonic balance. The first stage uses a modified conversion matrix approach to select the subharmonic loads of the active element enabling the frequency division by a given order N. The second stage makes use of an auxiliary generator to obtain and modify the sub-harmonic-power curve versus the input power or input frequency. Systematic simulation tools are used to eliminate common hysteresis phenomena, which require additional constraints to minimize the disturbance of the original frequency-division bands and output power. A harmonic-balance technique to distinguish between subcritical flip bifurcations, associated with hystereses, and supercritical ones is presented, to our knowledge, for the first time. A technique is also derived to transform subcritical bifurcations into supercritical ones. The techniques have been successfully applied to a frequency divider by 2 at 630 MHz. Index Terms--Bifurcation, conversion matrix, frequency divider, stability.

This paper focuses on anomalous nonlinear phenomena in a thyristor controlled reactor-static var compensator (TCR-SVC) system, called switching time bifurcation, and clarifies the relationship between the occurrence of nonlinear phenomenon and the intrinsic characteristics of the circuit equation with switching function. The occurrence of nonlinear phenomenon in a TCR-SVC system cannot be predicted when the dynamics of the circuit related to the switching action is neglected. Therefore, this paper considers the dynamics related to the switching operations in the analysis of nonlinear phenomena. The parametric excitation of circuit is discussed in relation to the homogeneous expression of the circuit equation. This paper indicates that the homogeneous equation of the TCR-SVC system results in Hill's equation, and it can be approximated as Mathieu's equation. The occurrence of nonlinear phenomena in the system is evaluated using the characteristics of Mathieu's equation. The anomalous nonlinear phenomena occur when the natural frequency of Mathieu's equation coincides with the frequency of the ac voltage in a TCR-SVC system. The parametric excitation is also confirmed through the characteristics of Hill's equation. This study clarified the interaction between the switching dynamics of the circuit and its external excitation, and clued the occurrence of nonlinear phenomena in the circuit. The proposed procedure can also be applied to the analysis for other switching converter circuits with periodic excitation source. Index Terms--Homogeneous equation, intrinsic oscillation, Mathieu's equation, nonlinear phenomenon, switching function, switching time bifurcation, TCR-SVC.

A maglev system with delayed acceleration feedback control is disturbed by the deflection of flexible guideway, and resonant response may take place. We have investigated sup-resonant response of the maglev system by employing center manifold reduction and the method of multiple scales. We present the dynamic model and expand it to a third-order Taylor series. Taking time delay as its bifurcation parameter, we discuss the condition for the occurring of Hopf bifurcation. We apply center manifold reduction to get the Poincare normal form of the nonlinear system and employ the perturbation technique to study sup-resonant response of the system. This yields the sup-resonant periodic solution of the normal form. We analyze the stability condition of the free oscillation in the solution and discuss the relatonship between guideway excitation and periodic solution. Finally, numerical results show how time delay, control, and excitation parameters affect the system response. With the proper system parameter, the free oscillation may vanish and only the periodic solution plays a part. Time delay can control amplitude of the forced oscillation. The appearance of the chaos phenomenon can also be governed by regulating time delay. And judiciously selecting a control parameter makes it possible to suppress the response. Index Terms--Chaos, delayed acceleration feedback control, Hopf bifurcation, nonautonomous maglev system, sup-resonant response.

This paper demonstrates a novel system-interrogation method based on observing the morphing of bifurcations and the postbifurcation dynamics through both experimental and numerical methods. A sensing cantilever beam is built with lead-zirconate-titanate patches symmetrically bonded to both sides of its root. A desired bifurcation in the dynamics of the beam can be induced by applying a nonlinear feedback excitation to the beam. The nonlinear feedback excitation requires the active measurement of the dynamics and a feedback loop, and it is generated by applying the voltage (resulting from a nonlinear feedback) to the piezoelectrode. Also, a finite element model is used to design the nonlinear feedback excitation and to predict the response of the sensing beam. Numerical simulations and experiments are performed and compared that demonstrate the effectiveness and high level of sensitivity of the novel approach to detect very small amounts of mass added at the tip of the beam.

This paper introduces an accurate transformer core model, using the Preisach theory, to represent the core magnetization characteristic. This modeling approach provides the required precision to match major and minor hysteresis loops of the model with those of the actual transformer core material. Using the proposed model, the ferroresonance phenomenon of a voltage transformer (VT) is simulated and compared to the corresponding experimental results. In addition, the simulated ferroresonance behavior of the VT based on: 1) the Electromagnetic Transients Program (EMTP)-RV hysteric reactor model, 2) the EMTP reactor type-96 model, and 3) a single-valued polynomial as magnetization characteristic, is also deduced and compared with the proposed model and the experimental results. The investigations conclude that the proposed model provides the most accurate results in terms of the VT core losses and the VT voltage waveforms and their peak values during 1) normal operating conditions, 2) ferroresonance transients and jumping from normal to ferroresonance operating conditions, and 3) ferroresonance steady-state conditions. Furthermore, higher accuracy of the proposed model in representing the hysteresis loop provides the highest and the most accurate bifurcation point and the transient loss when compared with other models. This paper also concludes that major and minor hysteresis loops must be represented in the core model to accurately simulate ferroresonance phenomenon of the VT. Index Terms--Bifurcation, ferroresonance, hysteresis, minor loops, power loss, Preisach theory, transformer.

When dealing with positive nonlinear systems, conventional theory requires too much for the stability of equilibrium points located on the boundary of the positive orthant, which encourages the consideration of stability with respect to the positive orthant. Generalizing this concept to the stability of a family of equilibrium points with Non-vanishing Basin of Attraction (NvBA)-stability has been introduced, which often becomes of interest when positive systems undergo bifurcations. In this technical note, we present a simple condition that can be employed for determining the NvBA-stability with respect to the positive orthant. The proposed condition is applicable to a class of nonlinear systems of certain Jacobian structure and is tailormade for this system. An illustrative example is included in order to help the exposition of the technical note. Index Terms--Basin of attraction, bifurcation, center manifold theorem, Lyapunov stability, positive systems.

An infinite-dimensional electromagnetic system is proposed as a practical model for analyzing the spatiotemporal chaos. The system consists of a linear lossless transmission line connected to a p-n-junction diode in series with a dc bias voltage source at one end and to an active linear resistor at the other end. The temporal dynamics of the backward-traveling voltage wave is investigated by using a corresponding one-dimensional map, and the effects of the serial dc bias voltage source on the dynamics of the system are particularly studied here. Numerical results are presented to show that the spatiotemporal nonlinear oscillation of the voltages along the lossless transmission line is the oscillation of isotropism with respect to space and time, and spatial intermittency and chaos exist in this infinite-dimensional electromagnetic system. Several spatiotemporal patterns of the voltages are also observed. Index Terms--Bifurcation, chaos, infinite-dimensional system, spatial intermittency, spatiotemporal pattern.

To study the stability of a nominal cyclic steady state in power electronic converters, it is necessary to obtain a linearization around the periodic orbit. In many past studies, this was achieved by explicitly deriving the Poincare map that describes the evolution of the state from one clock instant to the next and then locally linearizing the map at the fixed point. However, in many converters, the map cannot be derived in closed form, and therefore this approach cannot directly be applied. Alternatively, the orbital stability can be worked out by studying the evolution of perturbations about a nominal periodic orbit, and some studies along this line have also been reported. In this paper, we show that Filippov's method--which has commonly been applied to mechanical switching systems--can be used fruitfully in power electronic circuits to achieve the same end by describing the behavior of the system during the switchings. By combining this and the Floquet theory, it is possible to describe the stability of power electronic converters. We demonstrate the method using the example of a voltage-mode-controlled buck converter operating in continuous conduction mode. We find that the stability of a converter is strongly dependent upon the so-called saltation matrix--the state transition matrix relating the state just after the switching to that just before. We show that the Filippov approach, especially the structure of the saltation matrix, offers some additional insights on issues related to the stability of the orbit, like the recent observation that coupling with spurious signals coming from the environment causes intermittent subharmonic windows. Based on this approach, we also propose a new controller that can significantly extend the parameter range for nominal period-1 operation. Index Terms--Bifurcation, buck converter, differential inclusions, discontinuous systems, Filippov systems, power electronics.

The authors investigate a hybrid constant switching frequency current controller that uses both the turn-on and the turn-off current mode and the sliding mode control techniques. It is suitable for one-, two-, or four-quadrant operations and can be used with most topologies of dc--dc converters. It presents some advantages over the conventional peak current mode control. Indeed, it allows using low compensating slope without compromising the stability and it can work in the full range of the duty cycle values. Two methods are presented to study the characteristics of the proposed current controller. First, a high frequency small-signal average model is developed which takes into account the high switching frequency. It allows getting some basics design concerns such as overflow, time response and frequency behavior of the hybrid current controller. Second, a mathematical model derived from chaos theory is developed. It allows investigating the nature of the cycle described by the state trajectory, and determining the operating switching frequency of the current controller. Besides, it will be used to study its robustness properties according to loads parameters variations. Experimental results validate the theoretical approach and prove the effectiveness of this hybrid fixed frequency current controller. Index Terms--Bifurcation's diagram, Floquet multipliers, Jacobian's matrix, peak current mode control, Poincare's surface, sliding mode control, small-signal average model.

In this paper, stability and bifurcation of a general recurrent neural network with multiple time delays is considered, where all the variables of the network can be regarded as bifurcation parameters. It is found that Hopf bifurcation occurs when these parameters pass through some critical values where the conditions for local asymptotical stability of the equilibrium are not satisfied. By analyzing the characteristic equation and using the frequency domain method, the existence of Hopf bifurcation is proved. The stability of bifurcating periodic solutions is determined by the harmonic balance approach, Nyquist criterion, and graphic Hopf bifurcation theorem. Moreover, a critical condition is derived under which the stability is not guaranteed, thus a necessary and sufficient condition for ensuring the local asymptotical stability is well understood, and from which the essential dynamics of the delayed neural network are revealed. Finally, numerical results are given to verify the theoretical analysis, and some interesting phenomena are observed and reported. Index Terms--Hopf bifurcation, frequency domain approach, harmonic balance, recurrent neural network, stability.

Some practical models contain so complicated mathematical expressions that it is hard to determine the number and distribution of all equilibria, not mentioning the qualitative properties and bifurcations of those equilibria. The three-node recurrent neural network system with two free weight parameters, originally introduced by Rniz, Owens, and Townley in 1997, is such a system, for which the equation of equilibria involves transcendental function tanh(x) and its iterates. Not computing coordinates of its equilibria, in this paper, we display an effective technique to determine the number and distribution of its equilibria. Without full information about equilibria, our method enables to further study qualitative properties of those equilibria and discuss their saddle node, pitchfork, and Hopf bifurcations by approximating center manifolds. Index Terms--Bifurcation, center manifold, equilibrium, iteration, recurrent neural network, transcendental function.

Temperature rise may lead to strength degradation and stiffness deterioration of structures under fire conditions. The purpose of this paper is to theoretically study the thermal effect on the postbuckling behavior of an elastic or elastoplastic two-member truss, based on large-deformation elasticity considerations. Two kinds of loadings are considered, i.e., trusses under constant temperature but increasing roads, and trusses under constant loads but rising temperature. For the case with constant temperature, the critical load of an elastic truss will be greatly reduced if the effect of yielding is taken into account. Moreover, yielding of material can cause the truss to bifurcate from the original elastic path. For the case with constant loads, a critical temperature that occurs as the limit point of the temperaturedeflection curve can always be found. Besides, the presence of yielding can drastically reduce the critical temperature of an elastic truss, causing it to collapse in an abrupt manner. The solutions presented herein can be used as benchmarks for calibration of the accuracy of general finite-element procedures in analyzing structures under fire conditions. DOI: 10.1061/(ASCE)0733-9399(2008)134:4(330) CE Database subject headings: Bifurcations; Critical loads: Temperature; Postbuckling; Trusses; Thermal factors; Elasticity; Elastoplasticity.

Accurate prediction of shear band formation in geomaterials is crucial in the solution of various stability problems in geotechnical engineering. The initiation of shear band is strongly dependent on the constitutive description of the prelocalization homogeneous deformation. Conventional plasticity models assume that coaxiality exists between the directions of principal stresses and the directions of plastic strain increments. Accumulating evidence has however shown that this assumption is not appropriate. In this paper, a noncoaxial constitutive modeling platform is presented in a general three-dimensional stress space. It is shown that the classical vertex-like structure, which has been widely adopted to describe the noncoaxial constitutive response, only represents the two-dimensional condition. Examples are presented to demonstrate the capability of the modeling platform in capturing the initiation and orientation of shear band in a granular soil. The significance of the noncoaxiality effects is illustrated by comparisons of the predictions produced by coaxial and noncoaxial (both two-dimensional and three-dimensional) plasticity models. DOI: 10.1061/(ASCE)0733-9399(2008)134:4(322) CE Database subject headings: Bifurcations; Constitutive models; Three-dimensional models; Geomaterials; Plasticity.

In this paper, we give a detailed analytical study of a two-cell dc-dc buck converter. We analyse the dynamics of the system by using a discrete time modelling approach and considering a digital controller. This controller includes a dynamic compensator in the form of a digital integrator for the output variable regulation. The discrete time model for the whole system is used to predict the instability of the system when some design parameters are varied. To facilitate the design, an approximated closed form discrete time model is derived in the form of a recurrence equation which accurately describes the dynamical behavior of the system. The Jury test is applied to the characteristic polynomial in order to obtain stability boundaries in the design parameter space. Some design rules to obtain optimal transient behavior are also given. Numerical simulations and experimental measurements confirm the theoretical predictions. Index Terms--Bifurcations, discrete time model, digital pulsewidth modulation (PWM) control, stability analysis, two-cell dc-dc converters.

Nanomanipulation of biomolecules by using single-molecule methods and computer simulations has made it possible to visualize the energy landscape of biomolecules and the structures that are sampled during the folding process. We use simulations and single-molecule force spectroscopy to map the complex energy landscape of GFP that is used as a marker in cell biology and biotechnology. By engineering internal disulfide bonds at selected positions in the GFP structure, mechanical unfolding routes are precisely controlled, thus allowing us to infer features of the energy landscape of the wild-type GFP. To elucidate the structures of the unfolding pathways and reveal the multiple unfolding routes, the experimental results are complemented with simulations of a self-organized polymer (SOP) model of GFP. The SOP representation of proteins, which is a coarse-grained description of biomolecules, allows us to perform forced-induced simulations at loading rates and time scales that closely match those used in atomic force microscopy experiments. By using the combined approach, we show that forced unfolding of GFP involves a bifurcation in the pathways to the stretched state. After detachment of an N-terminal [alpha]-helix, unfolding proceeds along two distinct pathways. In the dominant pathway, unfolding starts from the detachment of the primary N-terminal [beta]-strand, while in the minor pathway rupture of the last, C-terminal [beta]-strand initiates the unfolding process. The combined approach has allowed us to map the features of the complex energy landscape of GFP including a characterization of the structures, albeit at a coarse-grained level, of the three metastable intermediates. AFM experiments | coarse-grained simulations | cross-link mutants | pathway bifurcation | plasticity of energy landscape

Byline: David J. Steigmann (Department of Mechanical Engineering, University of California, Berkeley, CA, 94720) Keywords: stability; bifurcation; elastic membranes Article note: 1. The associated Cauchy--Green deformation tensor C = Ft [...]

This paper describes a systematic methodology for complete stability analysis of nonlinear microwave multifunction circuits. The proposed strategy has two different stages: the stability analysis of a nominal steady-state solution and the use of continuation techniques to efficiently determine the unstable operation ranges. The stability analysis is demanding due to the multiple loops contained in the large multifunction circuit. The first step is to check the possible fulfillment of the oscillation startup conditions at different circuit nodes followed by pole-zero identification. Given the complexity of the circuit topology, a systematic technique is necessary for the selection of the observation nodes. This has been applied at both the lumped-element schematic and the layout levels. These stability analyses have been carried out at small-signal (linear) and large-signal (nonlinear) since the multifunction circuit includes a nonlinear mixer. In the case of instability, the origin of the oscillation and its characteristics are analyzed versus the critical circuit parameters through the application of continuation techniques to the steady-state oscillatory solution. Moreover, sensitivity yield analysis and variations of environmental conditions combined with the stability techniques have also been taken into account and integrated into the design cycle. The proposed systematic approach has been successfully applied to determine and correct an oscillation of a multifunction monolithic-microwave integrated-circuit converter. It has also been proven in other multifunction circuits in the same way. Index Terms--Bifurcation, continuation techniques, multifunction monolithic microwave integrated circuit (MMIC), stability analysis, stabilization.

The SPICE simulation program is widely used as a brute force simulator for analyzing and designing switching power converters. Results from SPICE are mostly useful, but their integrity is sometimes questionable as erroneous results could be obtained which may not reflect the true behavior of the circuits being simulated. Various parameters in SPICE are crucial in controlling the convergence and accuracy of the simulated results, e.g., relative error tolerance and maximum integration step size. In this paper, we study the system consisting of the SPICE simulation algorithm and the circuit being simulated. Specifically, we describe the generation of flawed solutions in terms of bifurcation of the system under parameter variations. Erroneous results have been collected for different relative error tolerances, maximum integration step sizes, and parasitic inductance and capacitance. These flawed solutions can be analyzed in terms of the manifestation of period-doubling bifurcation and chaotic behavior under variation of selected simulation parameters. This paper provides a systematic approach to rationalizing the behavior of the SPICE simulator, its practical significance being in the identification of the ranges of simulation parameters for which flawed solutions can be produced. Index Terms--Bifurcation, circuit simulation, power electronics, SPICE, switching converters.

4.1. Postponement of Bifurcation The influence of random fluctuations of the control parameter on the system's dynamic behavior near instability has been experimentally studied by many physicists (see, e.g., De [...]

The effects of coupled nonlinearities in the pitch and plunge degrees of freedom of an airfoil placed in a subsonic airflow are studied using a numerical time-marching scheme. The initial conditions are fixed, and the airfoil parameters are adopted from a previous study where primary and secondary Hopf bifurcations and modulated oscillations in a subcritical Hopf bifurcation were observed. The investigation is first carried out for fixed spring stiffness in the pitch degree of freedom while the plunge spring constant is varied. The second example fixes the plunge spring constant and varies the pitch spring stiffness. Both weak and strong restoring forces are considered. It is shown that coupled nonlinearities can generate a variety of motions and that chaotic behavior is possible in a narrow window of the bifurcation parameter.

A recent experiment [Vandenberghe, N., Zhang, J. & Childress, 5. (2004) J. Fluid Mech. 506, 147-155] has shown that an axle-mounted blade can spontaneously rotate when oscillated (or 'flapped') above a critical frequency in a fluid. To understand the nature of flapping locomotion we study numerically the dynamics of a simple body, flapped up and down within a viscous fluid and free to move horizontally. We show here that, at sufficiently large 'frequency Reynolds number,' unidirectional locomotion emerges as an attracting state for an initially nonlocomoting body. Locomotion is generated in two stages: first, the fluid field loses symmetry by an instability similar to the classical von Karman instability; and second, precipitous interactions with previously shed vortical structures 'push' the body into locomotion. Body mass and slenderness play central and unexpected roles in each stage. Conceptually, this work demonstrates how locomotion can be transduced from the simple oscillations of a body through an interaction with its fluid environment. bifurcation | flight | symmetry-breaking | instability | fluid-structure interaction

ABSTRACT--Many arterial diseases manifest at bifurcations, as for example, atherosclerosis and aneurysms. Findings over the last three decades reveal the important role of mechanics in the genesis and treatment of [...]

In this paper, we examine how varying the generation redispatch can improve the system stability margins with respect to Hopf bifurcations, as well as robustness to uncertainties in load modeling and distribution. It is seen that an optimal selection of load following units plays a key role in accomplishing these objectives. An optimal redispatch strategy is proposed, and is verified through a variety of experiments on the IEEE 39-bus system. Index Terms--Distributed slack bus, generation redispatch, Hopf bifurcations, stability.

The bifurcation structure of a simple power-system model is investigated, with respect to changes to both the real and reative loads. Numerical methods for this bifurcation analysis are presented and discussed. The model is shown to have a Bogdanov--Takens bifurcation point and hence homoclinic orbits; these orbits can be of Sil'nikov type with many coexisting periodic solutions. We may use the bifurcation calculations to divide the two-parameter plane into a number of regions, for which there are qualitatively different dynamics. We classify and further investigate the dynamical behavior in each of these regions, using a Monte Carlo method to investigate basins of attraction of various stable states. We then show how this classification can be used to denote each regions as either safe or unsafe with respect to the likelihood of voltage collapse. Index Terms--Basinofattraction, bifurcation, Bogdanov--Takens, continuation, dynamical system, homoclinic orbit, Monte Carlo, power system, shilnikov, Takens--Bogdanov, voltage collapse.

This paper proposes a method to trace bifurcation sets for a piecewise-defined differential equation. In this system, the trajectory is continuous, but it is not differentiable at break points of the characteristics. We define the Poincare mapping by suitable local sections and local mappings, and thereby it is possible to calculate bifurcation parameter values. As an illustrated example, we analyze the behavior of a two-dimensional nonlinear autonomous system whose state space is constrained on two half planes concerned with state-dependent switching characteristics. From investigation of bifurcation diagrams, we conclude that the tangent and global bifurcations play an important role for generating various periodic solutions and chaos. Some theoretical results are confirmed by laboratory experiments. Index Terms - Bifurcation, piecewise-defined differential equation, Poincare mapping.

This paper considers bifurcation phenomena in a simplified hysteresis neural network. The network consists of three cells and has three control parameters. We have discovered that the simple system exhibits various attractors: stable equilibria, periodic orbits, and chaos. Since the system is piecewise linear, the return map and Lyapunov exponents are calculated by using the piecewise exact solution. Using the mapping procedure, the bifurcation mechanism of stable equilibria and three kinds of bifurcation mechanisms of periodic orbits have been clarified. In addition, chaos has been analyzed by using Lyapunov exponents of the return map. Index Terms - Bifurcation, chaos, coupled oscillator, hysteresis, piecewise linear system.

This paper reports the occurrence of a rare phenomenon in dynamical systems when four different attractors namely a stable equilibrium, a stable limit cycle and two strange attractors coexist in a fundamental power system model. The paper shows that power system operation could get trapped into sustained chaotic oscillations after a large disturbance even when there exists a viable stable equilibrium point in the model. Index Terms - Bifurcations, chaos, nonlinear dynamics, power systems.

The postbuckling behavior of an elastic fixed-end column with an elastic brace at the center is investigated. Attention is focused on those of brace stiffness near its threshold value at which, under axial load, the column becomes critical with respect to two buckling modes simultaneously. We show that, for the brace stiffness greater than the threshold value, there are precisely two secondary bifurcation points on each primary postbuckling path bifurcating from one of the least two classical buckling loads, and the corresponding secondary postbuckling paths connect all of these secondary bifurcation points in a loop. For the brace stiffness less than the threshold value, no secondary bifurcation occurs. The asymptotic expansions of the primary and secondary postbuckling paths are constructed. The stability analysis indicates that, when the brace stiffness goes beyond its threshold value, the primary postbuckling path with a node in the center becomes unstable from stable by means of the secondary bifurcation (i.e., secondary buckling occurs).