Стохастическая чувствительность квазипериодических и хаотических аттракторов дискретной модели Лотки–Вольтерры

The aim of the study presented in this article is to analyze the possible dynamic modes of the deterministic and stochastic Lotka–Volterra model. Depending on the two parameters of the system, a map of regimes is constructed. Parametric areas of existence of stable equilibria, cycles, closed invariant curves, and also chaotic attractors are studied. The bifurcations such as the period doubling, Neimark–Sacker and the crisis are described. The complex shape of the basins of attraction of irregular attractors (closed invariant curve and chaos) is demonstrated. In addition to the deterministic system, the stochastic system, which describes the influence of external random influence, is discussed. Here, the key is to find the sensitivity of such complex attractors as a closed invariant curve and chaos. In the case of chaos, an algorithm to find critical lines giving the boundary of a chaotic attractor, is described. Based on the found function of stochastic sensitivity, confidence domains are constructed that allow us to describe the form of random states around a deterministic attractor. © Solid State Technology.All rights reserved.This study was supported by Russian Science Foundation, grant no. 16–11–10098

Влияние случайного воздействия на равновесные режимы модели популяционной динамики

In the paper, we study a dynamic model of interacting populations of the type “predator–two prey”. A detailed parametric analysis of the equilibrium modes arising in the system is carried out. In zones of the bifurcation parameter, where the coexistence of several equilibrium regimes is found, separable surfaces are constructed. Those surfaces are the boundaries of the attraction basins of different equilibria. It is shown that the effect of an external random disturbance can destroy the equilibrium mode of coexistence of three populations and lead to a qualitatively different mode of coexistence. Such qualitative changes lead to the extinction of one or two of the three populations. Using the technique of stochastic sensitivity function and the method of confidence domains, the probabilistic mechanisms of destruction of equilibrium modes are demonstrated. A parametric analysis of the probabilities of extinction of populations for two types is carried out. The range of the bifurcation parameter and the level of noise intensity, that are the most favorable for the coexistence of three populations, are discussed. © 2020 Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta. All rights reserved.This study was supported by the Russian Science Foundation, grant no. 16–11–10098

Evidence for Narrow N*(1685) Resonance in Quasifree Compton Scattering on the Neutron

The first study of quasi-free Compton scattering on the neutron in the energy range of $E_{\gamma}=0.75 - 1.5$ GeV is presented. The data reveals a narrow peak at $W\sim 1.685$ GeV. This result, being considered in conjunction with the recent evidence for a narrow structure at $W\sim 1.68$GeV in the $\eta$ photoproduction on the neutron, suggests the existence of a new nucleon resonance with unusual properties: the mass $M\sim 1.685$GeV, the narrow width $\Gamma \leq 30$MeV, and the much stronger photoexcitation on the neutron than on the proton.Comment: Replaced with the version published in Phys. Rev.

EQUILIBRIUM AND OSCILLATORY REGIMES IN AN AUTOCATALYTIC REACTOR WITH RANDOM PERTURBATION

The paper considers a stochastic model of thermokinetic reaction in a well-mixed reactor. A probabilistic analysis of complex oscillation modes is carried out. Noise-induced transitions, generation of high-amplitude oscillations, and the transition from regular to chaotic oscillations are described.Исследование выполнено при финансовой поддержке Министерства науки и высшего образования Российской Федерации в рамках Программы развития Уральского федерального университета имени первого Президента России Б.Н. Ельцина в соответствии с программой стратегического академического лидерства "Приоритет-2030"

Analysis of Noise-Induced Phenomena in a Multistable Consumer Network

The paper considers a stochastic consumer network. We study the parametric zone where the coexistence of several attractors is observed. The model is studied by direct numerical simulation methods and by using the stochastic sensitivity function. A description of noise-induced phenomena is given

Feasibility studies of the time-like proton electromagnetic form factor measurements with PANDA at FAIR

The possibility of measuring the proton electromagnetic form factors in the time-like region at FAIR with the \PANDA detector is discussed. Detailed simulations on signal efficiency for the annihilation of $\bar p +p$ into a lepton pair as well as for the most important background channels have been performed. It is shown that precision measurements of the differential cross section of the reaction $\bar p +p \to e^++ e^-$ can be obtained in a wide angular and kinematical range. The individual determination of the moduli of the electric and magnetic proton form factors will be possible up to a value of momentum transfer squared of $q^2\simeq 14$ (GeV/c)$^2$. The total $\bar p +p\to e^++e^-$ cross section will be measured up to $q^2\simeq 28$ (GeV/c)$^2$. The results obtained from simulated events are compared to the existing data. Sensitivity to the two photons exchange mechanism is also investigated.Comment: 12 pages, 4 tables, 8 figures Revised, added details on simulations, 4 tables, 9 figure

Technical Design Report for the PANDA Solenoid and Dipole Spectrometer Magnets

This document is the Technical Design Report covering the two large spectrometer magnets of the PANDA detector set-up. It shows the conceptual design of the magnets and their anticipated performance. It precedes the tender and procurement of the magnets and, hence, is subject to possible modifications arising during this process.Comment: 10 pages, 14MB, accepted by FAIR STI in May 2009, editors: Inti Lehmann (chair), Andrea Bersani, Yuri Lobanov, Jost Luehning, Jerzy Smyrski, Technical Coordiantor: Lars Schmitt, Bernd Lewandowski (deputy), Spokespersons: Ulrich Wiedner, Paola Gianotti (deputy

Measurement of the Longitudinal Spin Transfer to Lambda and Anti-Lambda Hyperons in Polarised Muon DIS

The longitudinal polarisation transfer from muons to lambda and anti-lambda hyperons, D_LL, has been studied in deep inelastic scattering off an unpolarised isoscalar target at the COMPASS experiment at CERN. The spin transfers to lambda and anti-lambda produced in the current fragmentation region exhibit different behaviours as a function of x and xF . The measured x and xF dependences of D^lambda_LL are compatible with zero, while D^anti-lambda_LL tends to increase with xF, reaching values of 0.4 - 0.5. The resulting average values are D^lambda_LL = -0.012 +- 0.047 +- 0.024 and D^anti-lambda_LL = 0.249 +- 0.056 +- 0.049. These results are discussed in the frame of recent model calculations.Comment: 13 pages, 7 figure

First Measurement of Chiral Dynamics in \pi^- \gamma -> \pi^- \pi^- \pi^+

The COMPASS collaboration at CERN has investigated the \pi^- \gamma -> \pi^- \pi^- \pi^+ reaction at center-of-momentum energy below five pion masses, sqrt(s) < 5 m(\pi), embedded in the Primakoff reaction of 190 GeV pions impinging on a lead target. Exchange of quasi-real photons is selected by isolating the sharp Coulomb peak observed at smallest momentum transfers, t' < 0.001 (GeV/c)^2. Using partial-wave analysis techniques, the scattering intensity of Coulomb production described in terms of chiral dynamics and its dependence on the 3\pi-invariant mass m(3\pi) = sqrt(s) were extracted. The absolute cross section was determined in seven bins of $\sqrt{s}$ with an overall precision of 20%. At leading order, the result is found to be in good agreement with the prediction of chiral perturbation theory over the whole energy range investigated.Comment: 10 pages, 5 figure

Feasibility studies of time-like proton electromagnetic form factors at PANDA at FAIR

Simulation results for future measurements of electromagnetic proton form factors at \PANDA (FAIR) within the PandaRoot software framework are reported. The statistical precision with which the proton form factors can be determined is estimated. The signal channel $\bar p p \to e^+ e^-$ is studied on the basis of two different but consistent procedures. The suppression of the main background channel, $\textit{i.e.}$ $\bar p p \to \pi^+ \pi^-$, is studied. Furthermore, the background versus signal efficiency, statistical and systematical uncertainties on the extracted proton form factors are evaluated using two different procedures. The results are consistent with those of a previous simulation study using an older, simplified framework. However, a slightly better precision is achieved in the PandaRoot study in a large range of momentum transfer, assuming the nominal beam conditions and detector performance