Position Of Bifurcation Point Research Articles

Моделирование и управление хаотическим процессом

The article investigates problems related to the control of the dynamics of a system given by the Henon map with a hysteresis component included in it. In particular, possible modifications of the limit set (attractor) of the modified Henon map under hysteresis conditions are studied. The hysteresis element is formalized based on design approach by means of the Preisach model, which is approximated by a system consisting of a finite set of non-ideal relays. To analyze the dynamics, numerical simulation is carried out for various values of the model parameters, which are characterized by chaotic dynamics. For this purpose, a Python script has been developed that simulates the dynamics of the system under hysteresis conditions, and also processes the results to identify dynamic modes. Based on the data obtained, a comparative analysis of strange attractors of the modified and classical Henot mappings is carried out. Next, we study the dynamics depending on the parameters of the modified Henon map. To detect various dynamic regimes, bifurcation diagrams were plotted, the high Lyapunov exponent was calculated based on the Rosenstein algorithm and the 0-1 test was produced depending on the system parameters, and the hysteresis nonlinearity parameter. Established, that hysteresis term regularize dynamics of the system compared to the classical map and changed in the position of bifurcation points in the space of system parameters.

New Classification for Bifurcated Mandibular Neural Canal

Objectives To analyze the occurrence rate of bifurcated mandibular canal (BMC) by cone beam CT(CBCT) and summarise a new classification for further clinical work and academic communication. Method Randomly collected the CBCT images of 350 adult patients. Firstly, we analysed and summarized the BMCs into four types by the position of bifurcation point in the mandible. Second, we did statistics about occurrence. Then we have measured three kinds of distance of Type I and Type II. At last, we compared the advantages and disadvantages about different classifications. Results Among these 350 patients, we found 110 adult people with BMC which indicated the occurrence rate of BMC was 31.43%. The most common type was Type I, especially Type IB, and the least was Type III. Vertical distance between the apex of the second molar, the third molar and mandibular canal are 4.36±2.51 mm and 2.45±2.23 mm. Distance from the apex of two molars to the bifurcated spot are 15.87±6.82mm and 9.32±5.37mm. And the distance between the apex and retromolar foramen in Type I are 22.19±5.97mm and 15.82±4.68mm. Conclusion Comparing with former typing theory, we summarized a new classification which is simpler and more convenient, which should attach scholars’ attention to BMC during clinical work.

Stability of axion dark matter-photon conversion

It is known that a coherently oscillating axion field is a candidate of the dark matter. In the presence of the oscillating axion, the photon can be resonantly produced through the parametric amplification. In the universe, there also exist cosmological magnetic fields which are coherent electromagnetic fields. In the presence of magnetic fields, an axion can be converted into a photon, and vice versa. Thus, it is interesting to investigate what happens for the axion-photon system in the presence of both the axion dark matter and the magnetic fields. This system can be regarded as a coupled system of the axion and the photon whose equations contain the Mathieu type terms. We find that the instability condition is changed in the presence of magnetic fields in contrast to the conventional Mathieu equation. The positions of bifurcation points between stable and unstable are shifted and new instability bands appear. This is because the resonantly amplified axion can be converted to photon, and vice versa.

Relationship between cancer mutations and parameter sensitivity in Rb pathway

It has long been known that formation of all sorts of tumors is largely owing to the genomic variations. Oncogenic mutations are often found focused on one or more important pathways which indicate that it is meaningful to investigate oncogenic mutations and oncogenic mechanisms from the point of view of biological network. Recently, we found that in apoptosis pathway of mammalian cell, mutations that cause large variations on the bifurcation point are more probably oncogenic mutations. Here, we used the Rb-E2F pathway in mammalian cell in response to growth factor as another example to verify this correlation. To conduct this study, nonlinear dynamics equations that describe the behavior of the Rb-E2F pathway was first constructed. Then we identified sensitive parameters which have a great influence on the system’s bifurcation point. And we found that the sensitive parameters are highly related to high-frequency oncogenic mutations after comparing the results of parameter sensitivity analysis with profile of known cancer mutations. Moreover, the position of bifurcation point rather than concentration of a certain protein is a better measurement to determine biological network's function. Our results further confirm that nonlinear dynamics analysis of biological networks is an important way to understand oncogenesis. And the analysis method can become a powerful tool to understand and analyze the function of biological network.

Nonlinear effects in a plane problem of the pure bending of an elastic rectangular panel

The paper presents a modification of the semi-inverse representation of the pure bending deformation of a prismatic panel with rectangular cross-section that is suitable for the method of successive approximations (or Signorinis expansion method). This modification was used to investigate with an accuracy to second order terms the plane problem of pure bending for three different models of nonlinearly elastic behavior: harmonic material, Blatz and Ko material, Murnaghan material. It was found that the typical diagram of bending has maximum point followed by falling region. To study the stability of the bent panel the bifurcation approach was used. Some results about the position of bifurcation points at the loading diagram depending on the material and geometrical parameters are presented.

Hopf bifurcation control of the Rössler system based on Washout filter controller

The Washout filter is adopted to control Hopf bifurcation in Rössler system. The effect of its parameters on the position of bifurcation point, the bifurcation type, and the amplitude of periodic solution is discussed in detail. Based on Routh criterion, the stability region in parameter space is found out firstly. Then the influence of the filter’s time constant and the linear gain on the location of bifurcation point is analyzed. By using the Direct Normal Form method, the normal form of the controlled Rössler system is deduced and the coefficient of resonant term is expressed as a function of the nonlinear gain. It is revealed that, by changing the sign and the absolute value of the real part of the coefficient, the nonlinear gain can modify the periodic solution’s amplitude and Hopf bifurcation type. All the results obtained are verified by numerical simulation.

Theoretical analysis of inhibition effect on steady states of enzymatic membrane reactor with substrate and product retention for reaction producing weak acid

The aim of this study is to formulate a model of enzymatic membrane reactor (EMR), i.e., a continuous, stirred tank bioreactor with full enzyme recycle, for a reaction producing a weak acid, and to explore the effect of substrate and product inhibition of different mechanisms coupled with transport properties of the membrane on the static behaviour of the system. The inhibition of an enzyme by a substrate leads to the non-monotonicity of reaction rate expression with respect to the substrate concentration. If a product of enzymatic reaction, taking place in the EMR, influences the pH of a reaction mixture this is also the factor causing the non-monotonicity of the substrate and product dependent reaction rate. The character of these dependencies affects substantially the structure of the steady states of the reactor. The bifurcation diagrams, shown in the work, are of different characters depending on the bifurcation parameter. It has been found, that bifurcation diagrams for competitive and uncompetitive inhibition by a substrate differ in the number and position of bifurcation points. Steady states of multiplicity five have been localised in case of uncompetitive inhibition by the substrate at high affinity of the enzyme to this substrate. Retention of reagents, related to transport properties of a membrane, influences significantly the effectiveness of a process. A specially written software in Delphi™ has been used for the calculations.