Interpreting a period-adding bifurcation scenario in neural bursting patterns using border-collision bifurcation in a discontinuous map of a slow control variable

To further identify the dynamics of the period-adding bifurcation scenarios observed in both biological experiment and simulations with differential Chay model, this paper fits a discontinuous map of a slow control variable of Chay model based on simulation results. The procedure of period adding bifurcation scenario from period k to period k ＋ 1 bursting （k = 1, 2, 3, 4） involved in the period-adding cascades and the stochastic effect of noise near each bifurcation point is also reproduced in the discontinuous map. Moreover, dynamics of the border-collision bifurcation is identified in the discontinuous map, which is employed to understand the experimentally observed period increment sequence. The simple discontinuous map is of practical importance in modeling of collective behaviours of neural populations like synchronization in large neural circuits.

Taming desynchronized bursting with delays in the Macaque cortical network

Inhibitory coupled bursting Hindmarsh-Rose neurons are considered as constitutive units of the Macaque corti- cal network. In the absence of information transmission delay the bursting activity is desynchronized, giving rise to spatiotemporally disordered dynamics. This paper shows that the introduction of finite delays can lead to the synchro- nization of bursting and thus to the emergence of coherent propagating fronts of excitation in the space-time domain. Moreover, it shows that the type of synchronous bursting is uniquely determined by the delay length, with the transi- tions from one type to the other occurring in a step-like manner depending on the delay. Interestingly, as the delay is tuned close to the transition points, the synchronization deteriorates, which implies the coexistence of different bursting attractors. These phenomena can be observed by different but fixed coupling strengths, thus indicating a new role for information transmission delays in realistic neuronal networks.

Detection of QTL for Cold Tolerance at Bud Bursting Stage Using Chromosome Segment Substitution Lines in Rice (Oryza sativa)

Ab The cold tolerance at the bud bursting stage （CTB） was evaluated at 5℃ by using a set of 95 chromosome segment substitution lines （CSSLs） derived from an indica rice 9311 and a japonica rice Nipponbare with a genetic background of 9311. The result showed that six CSSLs had slightly stronger effect on CTB than 9311. Total four quantitative trait loci （QTLs） for CTB were preliminary mapped on chromosomes 5 and 7 by substitution mapping, qCTB-5-1, qCTB-5-2 and qCTB-5-3 were mapped in the region of RM267-RM1237, RM2422-RM6054 and RM3321-RM1054, which were 21.3 cM, 27.4 cM and 12.7 cM in genetic distance on rice chromosome 5, respectively, qCTB-7 was mapped in a 6.8-cM region of RM11-RM2752 on rice chromosome 7.

Penetration depth for yaw-inducing bursting layer impacted by projectile

In order to accurately estimate the anti-penetration capacity of yaw-inducing bursting layer with irregular barriers on surface impacted by projectile,the theoretical model of attack angle and angular velocity for projectile impacting on irregular barrier was achieved according to the macroscopic relation of contact force versus contact time,in which the main factors such as the relative geometrical characteristics of projectile and irregular barrier,material property and impact velocity of projectile influencing on yaw-inducing effectiveness were considered.On the basis of considering synthetically the influences of attack angle,impact velocity,impact angle of projectile and uncontrolled free surface of target,the theoretical formulation of penetration depth for bursting layer with irregular barriers on surface impacted by projectile was presented by expressing the stress of an optional point on the nose of projectile according to the relation of stress versus velocity.The theoretical results indicate that in the case of oblique impact embodying effect of attack angle,the penetration depth is reduced with the increase of impact angle,attack angle or angular velocity,and penetration trajectory is also deflected obviously.The effectiveness of angular velocity influencing on penetration depth is increased with impact velocity increasing.The theoretical results are in good agreement with test data for low impact velocity.

Bursting oscillations in a hydro-turbine governing system with two time scales

A fast-slow coupled model of the hydro-turbine governing system （HTGS） is established by introducing frequency disturbance in this paper. Based on the proposed model, the performances of two time scales for bursting oscillations in the HTGS are investigated and the effect of periodic excitation of frequency disturbance is analyzed by using the bifurcation diagrams, time waveforms and phase portraits. We find that stability and operational characteristics of the HTGS change with the value of system parameter kd. Furthermore, the comparative analyses for the effect of the bursting oscillations on the system with different amplitudes of the periodic excitation a are carried out. Meanwhile, we obtain that the relative deviation of the mechanical torque mt rises with the increase of a. These methods and results of the study, combined with the performance of two time scales and the fast-slow coupled engineering model, provide some theoretical bases for investigating interesting physical phenomena of the engineering system.

Multi-stability involved mixed bursting within the coupled pre-Btzinger complex neurons

Neurons in the pre-B6tzinger complex within the mammalian brain stem play important roles in the generation of respiratory rhythms. Experimental observations show that some neurons can exhibit novel mixed bursting activities. In this paper, based on a mathematical model proposed by Butera, we show how the mixed bursting activities depend on the potassium current in the coupled pre-Botzinger complex. Using fast-slow decomposition and bifurcation analysis, we investigate the dynamics of mixed bursting, as well as the mechanisms of transition between different mixed bursting patterns. We find that mixed bursting involves different bistability, and it is the transition state of two types of regular burstings.

Bursting oscillation in CO oxidation with small excitation and the enveloping slow-fast analysis method

Based on the traditional scheme for a nonlinear system with multiple time scales, the enveloping slow-fast analysis method is developed in the paper, which can be employed to investigate the dynamics of nonlinear fields with multiple time scales with periodic excitation. Upon using the method, the behaviors of the kinetic model of CO oxidation on the platinum group metals have been explored in detail. Two typicM bursting phenomena such as Fold/Fold/Hopf bursting and Fold/Fold bursting, are presented, the bifurcation mechanisms of which have been obtained. Furthermore, the dynamic difference between the two cases corresponding to relatively large and small perturbation frequencies, respectively, has been presented, which can be used to describe the influence of the frequencies involving in the evolution on the bursting behaviors in the system.

Symmetric bursting behaviour in non-smooth Chua's circuit

The dynamics of a non-smooth electric circuit with an order gap between its parameters is investigated in this paper. Different types of symmetric bursting phenomena can be observed in numerical simulations. Their dynamical behaviours are discussed by means of slow-fast analysis. Furthermore, the generalized Jacobian matrix at the non-smooth boundaries is introduced to explore the bifurcation mechanism for the bursting solutions, which can also be used to account for the evolution of the complicated structures of the phase portraits. With the variation of the parameter, the periodic symmetric bursting can evolve into chaotic symmetric bursting via period-doubling bifurcation.

Acoustic characteristics of bubble bursting at the surface of a high-viscosity liquid

An acoustic pressure model of bubble bursting is proposed.An experiment studying the acoustic characteristics of the bursting bubble at the surface of a high-viscosity liquid is reported.It is found that the sudden bursting of a bubble at the high-viscosity liquid surface generates N-shape wave at first,then it transforms into a jet wave.The fundamental frequency of the acoustic signal caused by the bursting bubble decreases linearly as the bubble size increases.The results of the investigation can be used to understand the acoustic characteristics of bubble bursting.

Prediction of central bursting defects in rod extrusion process with upper bound analysis method

The prediction of central bursting defects in the rod extrusion process through conical dies using the upper bound analysisis investigated. A kinematically admissible velocity field, including the radial and angular velocity components, is proposed. A newcriterion is presented to predict the occurrence of the central bursting defects. Parameter bobt, which represents the risk probability ofcracking, is proposed. It is calculated using the shape of the boundary at the entrance by minimizing the total power dissipationduring the extrusion process. When bobt is equal to or greater than bcr, central bursting occurs. Furthermore, the quantitativerelationships between central bursting defects and process parameters （semi die angle, reduction in area and frictional factor） arestudied. The results show that the central bursting defects are affected primarily by the reduction in area and the friction factor. Thepresented criterion is verified by comparing with the FEM simulation data and the results of the published paper.

Bursting and spiking due to additional direct and stochastic currents in neuron models

Neurons at rest can exhibit diverse firing activities patterns in response to various external deterministic and random stimuli, especially additional currents. In this paper, neuronal firing patterns from bursting to spiking, induced by additional direct and stochastic currents, are explored in rest states corresponding to two values of the parameter VK in the Chay neuron system. Three cases are considered by numerical simulation and fast/slow dynamic analysis, in which only the direct current or the stochastic current exists, or the direct and stochastic currents coexist. Meanwhile, several important bursting patterns in neuronal experiments, such as the period-1 ＂circle/homoclinic＂ bursting and the integer multiple ＂fold/homoclinic＂ bursting with onc spike per burst, as well as the transition from integer multiple bursting to period-1 ＂circle/homoclinic＂ bursting and that from stochastic ＂Hopf/homoclinic＂ bursting to ＂Hopf/homoclinic＂ bursting, are investigated in detail.

Effect of magnetic flow and external forcing current on mixed bursting in the pre-Botzinger complex

The pre-B?tzinger complex(pre-B?tC) in mammalian brainstem is essential for the generation of respiratory rhythms.Most dynamic studies on the pre-B?tC neuron have been focused on its firing activities modulated by the ion conductances rather than that by the electromagnetic radiation or the external forcing current. In this paper, by adding the electromagnetic radiation and external forcing current to Park and Rubin’s model, we mainly investigate the influences of those two factors on the mixed bursting(MB) of single pre-B?tC neuron. First, we explore how the variation of external forcing current affects the MB patterns of the system with non-vanishing magnetic flux. We classify the MB patterns and show their dynamic mechanism through fast-slow decomposition and bifurcation analysis. Then, by modifying the feedback coefficient, we further analyze the sole effect of electromagnetic radiation on the firing activities of the system. Our results may be instructive in understanding the dynamical behavior of pre-B?tC neuron.

Effect of high-or low-speed fluctuations on the small-scale bursting events in an active control experiment

Active control of a fully developed turbulence boundary layer(TBL) over a flat plate has been investigated with a statistical view. The piezoelectric(PZT) oscillator is employed to produce periodic input into the inner region of the TBL.A wall probe is fixed upstream of the oscillator to identify the high-or low-speed fluctuations as the detecting signals.Then, the impact of the detecting signals on the small-scale bursting process is investigated based on the data acquired by the traversing probe downstream of the oscillator. The results indicate that the small-scale bursting intensity is restrained more apparently at high-speed detecting fluctuations but less impacted at low-speed detecting fluctuations. Furthermore, the perturbed-scale fluctuations arrange the small-scale bursting process in the near-wall region. The detecting signals have an obvious impact on this arrangement, especially the high-intensity regions of the small-scale bursting events: the vibration enhances the intensity at high-speed detecting signals but weakens it at low-speed detecting signals in these regions, which gives a direct evidence on how detecting signals interfering the small-scale bursting process.

ESTIMATE OF BURSTING PRESSURE OF MILD STEEL PRESSURE VESSEL AND PRESENTATION OF BURSTING FORMULA

In order to get more precise bursting pressure formula of mild steel, hundreds of bursting experiments of mild steel pressure vessels such as Q235（Gr.D） and 20R（1020） are done. Based on statistical data of bursting pressure and modification of Faupel formula, a more precise modified formula is given out according to the experimental data. It is proved to be more accurate after examining other bursting pressure value presented in many references. This bursting formula is very accurate in these experiments using pressure vessels with different diameter and shell thickness. Obviously, this modified bursting formula can be used in mild steel pressure vessels with different diameter and thickness of shell.

Research on experiment and calculation of foam bursting device

This research presents experimental data on mechanical foam bursting device,based on the high speed of air fluid impinging insidethe foam bursting device,foam bubbles disrupted as a consequence of pressures changed very quickly as shear force and their impact forces.Experimental data on foam-bursting capacity have been presented.Designed device can provide effective foam bursting on collapse foam.

The Effect of Atmospheric Oxygen on the Puffing and Bursting Phenomena during Vegetable Oils Droplets Vaporization Process for Their Use as Biofuel in Diesel Engine

The past literature on the use of vegetable oils as fuel in diesel engine revealed that utilizing vegetable oil fuels in diesel engines may require property changes in the oil or perhaps, some minor engine modifications or operating changes. This study was conducted to search for the effect of atmospheric oxygen on the puffing and bursting phenomena that occur during vegetable oils droplet vaporization process in their use as fuel in diesel engine. The fiber-suspended droplet technique was used, and the normalized square droplet diameter as well as the temperature evolution vicinity the droplet was analyzed. The results show that puffing and bursting phenomena highly depend on oxygen. In presence of atmospheric oxygen, there is an increase of the puffing and bursting intensity and therefore the evaporation rate of the vegetable oil droplets, but in an inert environment or when the environment is oxygen-depleted puffing and bursting phenomena disappearing and make place of a series of explosions with lower magnitude. The lack of oxygen reduces the thermal degradation, polymerization and oxidation reactions and consequently the vaporization rate of vegetable oils droplets;and could therefore lead to the formation of deposits in the form of polymers. This is unsuitable for their use as a fuel in diesel engines. It can also be concluded that atmospheric oxygen has some positive effects on engine performance and emissions when operating with vegetable oil. These results help to address the challenge for the use of alternative fuels such as non-edible vegetable oils.

Bursting phenomena as well as the bifurcation mechanism in a coupled BVP oscillator with periodic excitation

We explore the complicated bursting oscillations as well as the mechanism in a high-dimensional dynamical system.By introducing a periodically changed electrical power source in a coupled BVP oscillator, a fifth-order vector field with two scales in frequency domain is established when an order gap exists between the natural frequency and the exciting frequency.Upon the analysis of the generalized autonomous system, bifurcation sets are derived, which divide the parameter space into several regions associated with different types of dynamical behaviors. Two typical cases are focused on as examples,in which different types of bursting oscillations such as sub Hopf/sub Hopf burster, sub Hopf/fold-cycle burster, and doublefold/fold burster can be observed. By employing the transformed phase portraits, the bifurcation mechanism of the bursting oscillations is presented, which reveals that different bifurcations occurring at the transition between the quiescent states（QSs） and the repetitive spiking states（SPs） may result in different forms of bursting oscillations. Furthermore, because of the inertia of the movement, delay may exist between the locations of the bifurcation points on the trajectory and the bifurcation points obtained theoretically.

Three-Dimensional Bursting Phenomena in Meander Channel

Experiments were conducted in a U-shaped open-channel flume with the intention of investigating the bursting phenomena in the meander channel. The experimental results of the secondary flow fields and the Reynolds shear stress distributions show that the velocity and velocity fluctuation in the transverse direction are not negligible. Moreover, the bursting process is investigated using the three-dimensional quadrant analysis, which is more accurate than using the traditional two-dimensional quadrant analysis for the meandering channel. It is obtained from the experimental results that the internal group of events occurs more frequently than the external group, particularly the internal ejection and internal sweep events. In addition, the transition probabilities of the movements, which are defined as the changes of events from the current situation to the next situation in a time series, show that the stable organizations of events are the most possible movements, whereas the cross organizations of events have the least possible movements.

Bursting synchronization in clustered neuronal networks

Neuronal networks in the brain exhibit the modular （clustered） property, i.e., they are composed of certain subnetworks with differential internal and external connectivity. We investigate bursting synchronization in a clustered neuronal network. A transition to mutual-phase synchronization takes place on the bursting time scale of coupled neurons, while on the spiking time scale, they behave asynchronously. This synchronization transition can be induced by the variations of inter- and intra coupling strengths, as well as the probability of random links between different subnetworks. Considering that some pathological conditions are related with the synchronization of bursting neurons in the brain, we analyze the control of bursting synchronization by using a time-periodic external signal in the clustered neuronal network, Simulation results show a frequency locking tongue in the driving parameter plane, where bursting synchronization is maintained, even in the presence of external driving. Hence, effective synchronization suppression can be realized with the driving parameters outside the frequency locking region.

Delayed excitatory self-feedback-induced negative responses of complex neuronal bursting patterns

In traditional viewpoint,excitatory modulation always promotes neural firing activities.On contrary,the negative responses of complex bursting behaviors to excitatory self-feedback mediated by autapse with time delay are acquired in the present paper.Two representative bursting patterns which are identified respectively to be“Fold/Big Homoclinic”bursting and“Circle/Fold cycle”bursting with bifurcations are studied.For both burstings,excitatory modulation can induce less spikes per burst for suitable time delay and strength of the self-feedback/autapse,because the modulation can change the initial or termination phases of the burst.For the former bursting composed of quiescent state and burst,the mean firing frequency exhibits increase,due to that the quiescent state becomes much shorter than the burst.However,for the latter bursting pattern with more complex behavior which is depolarization block lying between burst and quiescent state,the firing frequency manifests decrease in a wide range of time delay and strength,because the duration of both depolarization block and quiescent state becomes long.Therefore,the decrease degree of spike number per burst is larger than that of the bursting period,which is the cause for the decrease of firing frequency.Such reduced bursting activity is explained with the relations between the bifurcation points of the fast subsystem and the bursting trajectory.The present paper provides novel examples of paradoxical phenomenon that the excitatory effect induces negative responses,which presents possible novel modulation measures and potential functions of excitatory self-feedback/autapse to reduce bursting activities.