Critical Bifurcation Point Research Articles

Coherence resonance and stochastic bifurcation behaviors of simplified standing-wave thermoacoustic systems.

In this work, noise-induced motions (i.e., external fluctuations) in two modelled standing-wave thermoacoustic systems are studied when these systems are close to the deterministic stability boundary. These systems include (1) open-open (i.e., Rijke-type) and (2) closed-open boundary conditions. It is found from the smooth transitions of the stationary probability density function that the thermoacoustic system is destabilized via stochastic P bifurcation, as the external noise intensity is continuously increased. In addition, the increased noise intensity can shift the hysteresis region, which makes the system more prone to quasi-periodic oscillations, but also reduces the hysteresis area. The noise-induced coherence motions are observed numerically in the open-open system, which is denoted by the occurrence of a bell-shaped signal to noise ratio (SNR). The SNR is shown to be applicable as a precursor. It becomes larger and the optimal noise intensity is decreased as the modelled thermoacoustic system approaches the critical bifurcation point. In addition, coherence resonance is observed in the closed-open system. To validate the findings, experimental studies are conducted on an open-open Rijke tube. Good qualitative agreements are obtained. The present study shed lights on the stochastic and coherence behaviors of the standing-wave thermoacoustic systems with different boundary conditions.

Bifurcation of critical points along gap-continuous families of subspaces

We consider the restriction of twice differentiable functionals on a Hilbert space to families of subspaces that vary continuously with respect to the gap metric. We study bifurcation of branches of critical points along these families and apply our results to semilinear systems of ordinary differential equations.

SOX17 Regulates Conversion of Human Fibroblasts Into Endothelial Cells and Erythroblasts by Dedifferentiation Into CD34+ Progenitor Cells.

The mechanisms underlying the dedifferentiation and lineage conversion of adult human fibroblasts into functional endothelial cells have not yet been fully defined. Furthermore, it is not known whether fibroblast dedifferentiation recapitulates the generation of multipotent progenitors during embryonic development, which give rise to endothelial and hematopoietic cell lineages. Here we established the role of the developmental transcription factor SOX17 in regulating the bilineage conversion of fibroblasts by the generation of intermediate progenitors. CD34+ progenitors were generated after the dedifferentiation of human adult dermal fibroblasts by overexpression of pluripotency transcription factors. Sorted CD34+ cells were transdifferentiated into induced endothelial cells and induced erythroblasts using lineage-specific growth factors. The therapeutic potential of the generated cells was assessed in an experimental model of myocardial infarction. Induced endothelial cells expressed specific endothelial cell surface markers and also exhibited the capacity for cell proliferation and neovascularization. Induced erythroblasts expressed erythroid surface markers and formed erythroid colonies. Endothelial lineage conversion was dependent on the upregulation of the developmental transcription factor SOX17, whereas suppression of SOX17 instead directed the cells toward an erythroid fate. Implantation of these human bipotential CD34+ progenitors into nonobese diabetic/severe combined immunodeficiency (NOD-SCID) mice resulted in the formation of microvessels derived from human fibroblasts perfused with mouse and human erythrocytes. Endothelial cells generated from human fibroblasts also showed upregulation of telomerase. Cell implantation markedly improved vascularity and cardiac function after myocardial infarction without any evidence of teratoma formation. Dedifferentiation of fibroblasts to intermediate CD34+ progenitors gives rise to endothelial cells and erythroblasts in a SOX17-dependent manner. These findings identify the intermediate CD34+ progenitor state as a critical bifurcation point, which can be tuned to generate functional blood vessels or erythrocytes and salvage ischemic tissue.

Coherence resonance and stochastic bifurcation in standing-wave thermoacoustic systems

In this work, we develop a noisy nonlinear model and conduct experimental tests to study the stochastic bifurcation and coherence resonance in standing-wave thermoacoustic systems. When white Gaussian noise is added and its intensity is varied, it is found that the stochastic behaviors of the system can be better described by stochastic P bifurcation. When the noise intensity is chosen as a bifurcation parameter, it is shown to the bi-modal region and reduce the bi-modal area are shifted. In addition, the noise-induced coherence motions are examined and confirmed. Resonance-like behaviors of signal to noise ratio (SNR) are clearly observed. When the system approaches the critical bifurcation point, SNR is found to become larger and the optimal noise intensity is decreased to a smaller value. This property can be used as a precursor to the Hopf bifurcation in standing-wave thermoacoustic systems. Experiments are then conducted on a Rijke-type thermoacoustic system with 3 loudspeakers implemented. Transition to instability is found to be subcritical. Comparison is then made between the present theoretical and experimental results. Good qualitative agreements are obtained in terms of (1) SNR, (2) the peak height of power spectrum, and (3) the width of the frequency.

Numerical modeling of concrete beams under serviceability conditions with a discrete crack approach and noniterative solution‐finding algorithms

This paper describes the development and validation of a comprehensive numerical model enabling the simulation of reinforced concrete beams under serviceability conditions using a discrete crack approach. The highly nonlinear behavior introduced by the different material models and the many localized cracks propagating within the member pose a challenge to classic iterative solvers, which often fail to converge. This limitation is solved using a noniterative solution-finding algorithm to overcome critical bifurcation points. The finite element model was validated using experimental data on lightweight aggregate concrete beams under flexural loading. It was shown that the model properly simulates both the overall and localized features of the structural response, including curvature, crack openings, and crack patterns. The model was used to carry out a numerical study of the role of longitudinal reinforcement ratios and crack widths in reinforced concrete beams. It was observed that the total crack openings along a member seem to remain nearly independent of the tensile reinforcement for ratios >2.5% and the same level of strength.

Large amplitude and multiple stable periodic oscillations in treatment-donation-stockpile dynamics

A transmission–treatment–donation–stockpile model was originally formulated for the 2014–2015 West Africa Ebola outbreak in order to inform policy complication of large scale use and collection of convalescent blood as an empiric treatment. Here we reduce this model to a three dimensional system with a single delay counting for the duration between two consecutive donations. The blood unit reproduction number R0 is calculated and interpreted biologically. Using the LaSalle’s invariance principle we show that the zero blood bank storage equilibrium is globally asymptotically stable if R0 1, the system has a non-zero equilibrium with potential occurrence of Hopf bifurcations. The geometric approach previously developed is applied to guide the location of critical bifurcation points. Numerical analysis shows that variations of the single delay parameter can trigger bi-stable large amplitude periodic solutions. We therefore suggest that this time lag must be carefully chosen and maintained to attain stable treatment availability during outbreaks.

Nonlinear aero-thermal flutter postponement of supersonic laminated composite beams with shape memory alloys

Abstract The nonlinear aerothermal flutter instability of a shape memory alloy (SMA) fiber reinforced composite beam subjected to simultaneous actions of thermal and aerodynamic loads is investigated. The Brinson model is used to simulate behaviors of the SMA fibers and the Euler-Bernoulli beam theory along with nonlinear von-Karman strain field are used for modeling of the beam. Thermomechanical properties are assumed to be temperature-dependent. The aerodynamic pressure is modeled based on the quasi-steady first-order piston theory. The governing equations are solved by means of the Galerkin approach, and flutter and buckling boundaries, natural frequencies and damping ratios are obtained. Effects of various pivotal factors such as SMA volume fraction, prestrain of SMA fibers, location and orientation of SMA fibers on critical flutter dynamic pressure, damping ratio and bifurcation points and paths are studied. The results show that the aerothermal flutter characteristics of the laminated beam can be significantly enhanced by embedding SMA fibers. Moreover, the presence of aerodynamic flow and SMA fibers results in postponement of the bifurcation point and a reduction of the postbuckling deflection. The results of this study are expected to shed a light into enhancing the stability boundaries efficiently by increasing the SMA fiber volume fraction and prestrain.

Post-buckling and Large Amplitude Free Vibration Analysis of Composite Beams: Simple Intuitive Formulation

Post-buckling and large amplitude free vibration analysis of composite beams with axially immovable ends is investigated in the present study using a simple intuitive formulation. Geometric nonlinearity of Von-Karman type is considered in the analysis which accounts for mid-plane stretching action of the beam. Intuitive formulation uses only two parameters: the critical bifurcation point and the axial stretching force developed due to membrane stretching action of the beam. Hinged–hinged, clamped–clamped and clamped–hinged boundary conditions are considered. Numerical accuracy of the proposed analytical closed-form solutions obtained from the intuitive formulation are compared to available finite element solutions for symmetric and asymmetric layup schemes of laminated composite beam which indicates the confidence gained on the present formulation.

Neimark-Sacker Bifurcation of Rolling Bearing System with Fault in Outer Ring

Piecewise non-smooth model of three-degree-of-freedom rolling bearing system with fault in outer Ring is established by the method of the nonlinear theory. The Neimark-Sacker bifurcation of bearing system is first studied in this paper. The switching matrixes of system are obtained at the switching boundaries, and theNeimark-Sacker bifurcation of non-smooth bearing system is analyzed by combining the switching matrixes with the Floquet theory for smooth systems. The numerical method is used to further reveal the Neimark-Sacker bifurcation of bearing system through establishing the Poincare mapping on the collision plane. When the rotating frequency is increased to reach the critical bifurcation point, a pair of complex conjugate Floquet multipliers is on the unit circle and others into a unit circle , and the Neimark-Sacker bifurcation appears.The study of bifurcation of the fault bearing system provides reliable basis for the design and fault diagnosis and provides theoretical guidance and technical support for the actual design in the safe and stable operation of large high-speed rotating machinery.

Nonequilibrium scaling explorations on a two-dimensional Z(5)-symmetric model.

We have investigated the dynamic critical behavior of the two-dimensional Z(5)-symmetric spin model by using short-time Monte Carlo (MC) simulations. We have obtained estimates of some critical points in its rich phase diagram and included, among the usual critical lines the study of first-order (weak) transition by looking into the order-disorder phase transition. In addition, we also investigated the soft-disorder phase transition by considering empiric methods. A study of the behavior of β/νz along the self-dual critical line has been performed and special attention has been devoted to the critical bifurcation point, or Fateev-Zamolodchikov (FZ) point. First, by using a refinement method and taking into account simulations out of equilibrium, we were able to localize parameters of this point. In a second part of our study, we turned our attention to the behavior of the model at the early stage of its time evolution in order to find the dynamic critical exponent z as well as the static critical exponents β and ν of the FZ point on square lattices. The values of the static critical exponents and parameters are in good agreement with the exact results, and the dynamic critical exponent z≈2.28 very close to the four-state Potts model (z≈2.29).

Bifurcation analysis of anti-phase oscillations and synchrony in the tadpole central pattern generator

Recent experimental findings in the laboratory of Wen-Chang Li (St. Andrews University, UK) demonstrate that the same neural Central Pattern Generator (CPG) within the hindbrain/spinal cord of the Xenopus tadpole can produce both reliable anti-phase oscillations between the left and right sides of the body (swimming) and long bouts of in-phase synchronous activity. The key element of the CPG circuit includes a pair of neurons on each side of the body at about the same position: an excitatory descending interneuron (dIN) and an inhibitory commissural interneuron (cIN). A simplified description of the CPG activity in swimming regime follows from experimental facts: dIN spiking on one side leads to excitation of the cIN on the same side, which inhibits the dIN on the opposite side causing a spike due to post-inhibitory rebound (PIR). Similarly, experiments suggest that synchrony appears as a result of simultaneous firing of dINs on both sides which leads to simultaneous firing of cINs on both sides, followed by inhibition of dINs (on opposite sides) and a new cycle of simultaneous dIN firing due to PIR. To study these exciting experimental findings we use biologically realistic anatomical and functional computational models [1-3]. The tadpole swimming model represents a 1.5 mm section of tadpole spinal cord with ~ 1,500 neurons, interconnected by ~ 85,000 synapses. Neuron dynamics are simulated according to a conductance based model of the Hodgkin-Huxley type. Additionally, gap junctions between dINs within 100µm of each other in the rostro-caudal direction are included. From studying the dynamics of this model and bifurcation analysis of the key element of the CPG circuit, we conclude: 1. There are two limit cycles in the phase space of the model: an anti-phase limit cycle with period T which corresponds to swimming activity, and an in-phase limit cycle with period T/2 which corresponds to synchrony (see Figure ​Figure11). Figure 1 Phase portraits of the system during anti-phase (green) and in-phase (blue) activity. Horizontal and vertical axes correspond to membrane potentials of dINs at similar positions on the left and right body side respectively. 2. The anti-phase (swimming) cycle is stable and robust with a large basin of attraction. The in-phase (synchrony) cycle can be initiated from swimming regime by mid-cycle stimulation of dIN neurons, but is generally unstable or has a very small basin of attraction. 3. The in-phase cycle is near a fold of limit cycles bifurcation. For a minority of generated connections the stable in-phase limit cycle exists. However, for most connections this stable cycle does not exist, although its “ghost” is still visible: after several synchronous cycles the system returns to swimming oscillations. 4. The stability of synchrony is extremely sensitive to the synaptic/conductance delays between dINs and cINs, with longer delays stabilizing synchrony. 5. It is unclear whether synchrony has a functional purpose. If it does, we hypothesize that in this early developmental stage the system may be near to the critical bifurcation point in order to provide flexibility in locomotion control. As the tadpole develops, longer synaptic delays may act to stabilize the synchronous firing pattern.

STABILITY AND NONLINEAR DYNAMIC ANALYSES OF BEAM WITH PIEZOELECTRIC ACTUATOR AND SENSOR BASED ON HIGHER-ORDER MULTIPLE SCALES METHODS

Higher-order multiple scales methods have been developed for a strong nonlinear differential equation modeling the nonlinear transverse dynamic behavior of piezoelectric–elastic–piezoelectric sandwich beams. The proportional and derivative potential feedback controls via sensor and actuator layers are used. Two higher-orders multiple scales methods are developed leading to accurate approximate time-response and frequency and phase-amplitude relationships. As the classical multiple scales method disregards the quadratic nonlinear terms, the developed higher-order multiple scales methods overcame this drawback and lead to more accurate results. Static and dynamic stability criteria are elaborated and tested. Critical bifurcation points and peak amplitudes are characterized in accordance with the excitation amplitude and the feedback parameters.

Critical points and points of the bifurcation of the rotating magnetized newtonian polytropes with a 1 ⩽ n ⩽ 1.6 index

The presence of critical points and the bifurcation points of rotating Newtonian polytropes with an index of 1 ⩽ n ⩽ 1.6 has been shown for the first time in this paper. The symbolic-numerical calculation error in metric L2 has reached the size of the 10−4 order. The approximate analytical solution to the problem to the abovementioned accuracy has been set forth. A critical value of the polytropes index n = nk = 1.51025 has been calculated which is the highest among the critical points and bifurcation points. The value nk corresponds to the infinitely slow polytropes rotation. Furthermore, in this paper the presence of the period jump at the bifurcation point Tb has been predicted and the relative value of this jump ΔTb/Tb ∼ B0in4/3 has been estimated.

The impact of Typhoon Jangmi (2008) on the midlatitude flow. Part II: Downstream evolution

AbstractExtratropical transition (ET) of a tropical cyclone (TC) can modify the midlatitude flow and thus have implications for the weather and predictability in downstream regions such as North America or Europe. Albeit recurving and undergoing ET, the downstream impact of Typhoon Jangmi in September 2008 during the THORPEX Pacific Asian Regional Campaign (T‐PARC) was weak. In this study, we explore the physical processes inhibiting the reintensification of Jangmi and governing the forecast uncertainty during ET. The focus is on the relative contribution of the TC and the midlatitude flow. Quasi‐geostrophic diagnostics reveal that Jangmi is located south of and in phase with a midlatitude trough. Jangmi does not couple with the region favourable for reintensification ahead of the trough and subsequently decays. Instead, a weak frontal wave‐like cyclone develops. The role of the phasing of Typhoon Jangmi and the midlatitude Rossby wave pattern is tested in sensitivity experiments with the COSMO model in which Jangmi has been relocated. The simulations reveal two contrasting groups of scenarios. The first group reflects the weak actual ET and subsequent decay accompanied by a broad ridge over the Pacific. The second group is characterized by a strong ET with extratropical reintensification, the triggering of a pronounced Rossby wave train and downstream cyclogenesis. The displacement of Jangmi's initial position in the two contrasting groups is less than 1.25° (130 km). In the frame moving with the environmental background flow a critical bifurcation point for the track of Jangmi exists. The relative position to this bifurcation point determines whether Jangmi decays or reintensifies and triggers a Rossby wave train. A simple discrimination parameter is derived that allows for classifying the scenarios. The observed behaviour gives a simple explanation for the reduced predictability of the track and of the midlatitude flow in downstream regions during ET.

Bifurcation of Critical Points for Solutions of the 2D Euler and 2D Quasi-geostrophic Equations

We consider the 2D Euler and 2D quasi-geostrophic equations with periodic boundary conditions. For both systems we will use the stream-function formulation and study the bifurcation problem for the critical points of the stream function. In a small neighborhood of the origin, we construct a set of initial data such that initial critical points of the stream function bifurcate from 1 to 2 and then to 3 critical points in finite time. For the quasi-geostrophic equation the whole bifurcation process takes place strictly within the lifespan of the constructed local solution.

Modeling the effects of climate change on eelgrass stability and resilience: future scenarios and leading indicators of collapse

Seagrass meadows influence local hydrodynamics in coastal bays, resulting in a decrease in the shear stress acting on the underlying bed sediment. The reduced sediment suspension and water column turbidity creates a more favorable light environment for further seagrass growth. This positive feedback is strong enough to induce depth-dependent bistable dynamics with 2 possible stable states, an extant meadow and a bare sediment surface. A coupled vegetation-growth hydrodynamic model was used to investigate eelgrass stability and leading indicators of ecosystem shift under the effects of sea-level rise and increases in water temperature associated with climate change. The model was applied to Hog Island Bay, a shallow coastal bay within the Virginia Coast Reserve, USA, where eelgrass restoration efforts are ongoing. The results indicate that while extant eelgrass meadows are likely to tolerate sea-level rise, an increase in the frequency of days when summer water temperature exceeds 30°C will cause more frequent summer die-offs. This increase in the number of higher temperature disturbance events is likely to push a dense meadow initially located within the bistable depth range (1.6 to 1.8 m mean sea level) toward and eventually past a critical bifurcation point, from which recovery is not possible. We identified 2 leading indicators of a meadow nearing this bifurcation point, both associated with the number of leaves per shoot: ‘flickering,’ which reflects conspicuous fluctuations from one attractor to the other across the threshold, and ‘slowing down,’ which is the decreased recovery from perturbations as a system gets close to a threshold. Our model indicates that the eelgrass in these coastal bays has limited resilience to increases in water temperatures predicted from current climate change models.

New Bifurcation Critical Criterion of Flip‐Neimark‐Sacker Bifurcations for Two‐Parameterized Family of n‐Dimensional Discrete Systems

A new bifurcation critical criterion of flip‐Neimark‐Sacker bifurcation is proposed for detecting or anticontrolling this type of codimension‐two bifurcation of discrete systems in a general sense. The criterion is built on the properties of coefficients of characteristic equations instead of the properties of eigenvalues of Jacobian matrix of nonlinear system, which is formulated using a set of simple equalities and inequalities consisting of the coefficients of characteristic polynomial equation. The inequality conditions enable us to easily pick off the fake parameter domain whereas the equality conditions are used to accurately locate the critical bifurcation point. In particular, after the bifurcation parameter piont is determined, the inequality conditions can be used to figure out the feasible region of other system parameters. Thus, the criterion is suitable for two‐parameterized family of n‐dimensional discrete systems. As compared with the classical critical criterion (or definition) of flip‐Neimark‐Sacker bifurcation stated in terms of the properties of eigenvalues, the proposed criterion is preferable in anticontrolling or detecting the existence of flip‐Neimark‐Sacker bifurcation in high‐dimension nonlinear systems, due to its explicit parameter mechanism of the bifurcation.

Time-varying gain modulation on neural circuit dynamics and performance in perceptual decisions

Recent studies have shown that urgency signals may play an important role during the temporal integration of sensory evidence in perceptual decision-making. Furthermore, it has been shown that neurons in the lateral intraparietal area (LIP) can exhibit temporal integration properties in perceptual decision-making tasks, as well as multiplicative gain modulation properties. Our theoretical work connects this growing body of research areas. We investigate how time-varying single-cell gain modulation affects the network dynamics of a biological neural circuit model (Wong, Huk, Shadlen and Wang, 2007) for motion-discrimination tasks. Since we are interested in two-alternative forced-choice tasks, we implement a three-population network model. Two populations of excitatory pyramidal cells are selective to the coherent motion directions in a random dot motion-discrimination task. A third population of interneurons mediates pooled inhibition. We use dynamical systems analyses to study how the network dynamics evolves over different epochs of a trial. In order to enable categorical choice, the two selective populations need to remain at a common stable high firing-rate during the target-period prior to the motion stimulus onset. In reaction time (RT) tasks, the firing-rates typically diverge at a higher firing-rate shortly after motion stimulus onset (e.g. Roitman and Shadlen, 2002; Huk and Shadlen, 2005). Our analyses reveal that increasing the gains of both excitatory and inhibitory neurons is necessary to permit such neuronal dynamics to occur; an unstable saddle steady-state (that causes the divergence) has to be higher than the stable firing-rate during the target-period. In addition, the network is required to operate near a critical bifurcation point. Simulating our model, we are able to strikingly capture the full characteristics of the LIP neuronal dynamics in motion-discrimination tasks more accurately than past models, while accurately reproducing the behavioral data. Our model is also able to reproduce the timecourse of neuronal firing-rates in the fixed-viewing duration (FD) version of this task (e.g. Shadlen and Newsome 2001; Roitman and Shadlen 2002). It has been observed that in the FD task, the firing-rates of the selective populations are lower, and diverge from a level lower than during the target-period, contrary to that in the RT version. Firing-rates are also typically lower than the decision threshold during the delay-period in FD task. These phenomena can be accommodated in the same model by having lower gains than in the RT task. This approach is consistent with the intuition that decision-making that aims to maximize reward-rate (total number of correct responses over total time taken), by optimizing a speed-accuracy tradeoff in a RT task, would be more demanding and therefore involve more attentional resources than decision-making in a FD task, where the reward is dependent only on accuracy. In fact, our simulations predict that a short time-constant of gain modulation, e.g. indicating fast attentional modulation, enables the maximum reward rate to be attained. Our model thus provides an integrative and coherent understanding of the interplay among separate neuronal processes to enable flexible and optimal decision performance.

Emerging Insights into the Molecular Pathogenesis of Uveal Melanoma

Uveal melanoma is the most common primary cancer of the eye, and often results not only in vision loss, but also in metastatic death in up to half of patients. For many years, the details of the molecular pathogenesis of uveal melanoma remained elusive. In the past decade, however, many of these details have emerged to reveal a fascinating and complex story of how the primary tumor evolves and progresses. Early events that disrupt cell cycle and apoptotic control lead to malignant transformation and proliferation of uveal melanocytes. Later, the growing tumor encounters a critical bifurcation point, where it progresses along one of two genetic pathways with very distinct genetic signatures (monosomy 3 vs 6p gain) and metastatic propensity. Late genetic events are characterized by increasing aneuploidy, most of which is nonspecific. However, specific chromosomal alterations, such as loss of chromosome 8p, can hasten the onset of metastasis in susceptible tumors. Taken together, this pathogenetic scheme can be used to construct a molecularly based and prognostically relevant classification of uveal melanomas that can be used clinically for personalized patient management.

Asymmetric periodic orbits in the photogravitational Copenhagen problem

In this paper we study the O x -asymmetric solutions of the planar photogravitational restricted three-body problem in the case of primaries with equal masses and equal values of the radiation pressure parameters. In particular, we are concerned with the families of asymmetric orbits which bifurcate from the well known families a, b, and c. Their evolution is examined via the numerical construction of series of the critical bifurcation points of a, b, and c with respect to the variation of the common radiation parameter q . We also present some illustrative cases of these families for several values of this parameter. In order to avoid the singularity due to binary collisions between the third body and one of the primaries, the equations of motion of the problem are regularized by using the Levi-Civita transformations.