Noise-induced behavioral change driven by transient chaos

We study behavioral change in the context of a stochastic, non-linear consumption model with preference adjusting, interdependent agents. Changes in long-run consumption behavior are modelled as noise induced transitions between coexisting attractors. A particular case of multistability is considered: two fixed points, whose immediate basins have smooth boundaries, coexist with a periodic attractor, with a fractal immediate basin boundary. If a trajectory leaves an immediate basin, it enters a set of complexly intertwined basins for which final state uncertainty prevails. The standard approach to predicting transition events rooted in the stochastic sensitivity function technique due to Mil'shtein and Ryashko (1995) does not apply since the required exponentially stable attractor, for which a confidence region could be constructed, does not exist. To solve the prediction problem we propose a heuristic based on the idea that a vague manifestation of a non-attracting chaotic set (chaotic repellor) - could serve as a surrogate for an attractor. A representation of the surrogate is generated via an algorithm for generating the boundary of an absorbing area due to Mira et al. (1996). Then a confidence domain for the surrogate is generated using the approach due to Bashkirtseva and Ryashko (2019). The intersections between this confidence region and the immediate basins of the coexisting attractors can then be used to make predictions about transition events. Preliminary assessments show that the heuristic indeed explains the transition probabilities observed in numerical experiments. © 2022 The Authors075-02-2022-877; Ministry of Education and Science of the Russian Federation, MinobrnaukaTatyana Perevalova and Jochen Jungeilges gratefully acknowledges research funding from the Ministry of Science and Higher Education of the Russian Federation (Ural Mathematical Center project No. 075-02-2022-877 )

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

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

Asset Price Dynamics in a “Bull and Bear Market”

We generalize an existing asset market model with heterogenous agents. In particular, we consider the case in which no-trade and low-trade intervals of chartists and fundamentalists respectively are not congruent. Thus we model chartist and fundamentalists who respond to asset prices in agent-specific neighborhoods around the fundamental value with different trade intensities. The resulting asset price dynamics is generated by a one-dimensional 5-piece linear map with discontinuities. Our analysis of this map focusses on coexisting price equilibria. Conditions for their existence and stability are determined analytically. By visualizing the results we allow for a basic bifurcation analysis in a 4-dimensional parameter space. According to our findings the extent of the disparity between the no-trade and low-intervals effects the existence of equilibria but not their stability. © 2020

Transitions between Metastable Long-Run Consumption Behaviors in a Stochastic Peer-Driven Consumer Network

We study behavioral change - as a transition between coexisting attractors - in the context of a stochastic, non-linear consumption model with interdependent agents. Relying on the indirect approach to the analysis of a stochastic dynamic system, and employing a mix of analytical, numerical and graphical techniques, we identify conditions under which such transitions are likely to occur. The stochastic analysis depends crucially on the stochastic sensitivity function technique as it can be applied to the stochastic analoga of closed invariant curves [14], [1]. We find that in a moderate noise environment increased peer influence actually reduces the complexity of observable long-run consumer behavior. © 2021 American Institute of Mathematical Sciences. All rights reserved.Acknowledgments. Tatyana Perevalova and Jochen Jungeilges gratefully acknowledge research funding from the Ministry of Science and Higher Education of the Russian Federation (Ural Mathematical Center project No. 075-02-2021-1387)

Parity and Time Reversal in J/Psi Decay

With the prospect of large numbers of $J/\Psi$ decay events becoming available in the near future, it is interesting to search for symmetry violating effects as probes of new physics and tests of the standard model. $J/\Psi$ decay events could provide the first observation of weak effects in otherwise strongly decaying particles. We calculate a T odd asymmetry in the $J/\Psi$ decay into photon plus lepton pair due to Z boson exchange. Extensions to hadronic final states are also discussed.Comment: 9 pages, 3 eps figures revised to include additional relevant reference

Computer Modeling and Analisis of Multistability in an Interaction Between Two Consumers Model

В работе рассматривается дискретная модель, которая описывает динамику взаимодействия двух потребителей. В рамках детерминированного анализа была изучена зона сосуществования как минимум двух равновесий. Были определены зоны сосуществования трех и более устойчивых аттракторов, описаны бифуркационные сценарии. Показана фрактальная структура бассейнов притяжения аттракторов. Было изучено воздействие на систему аддитивного и параметрического шумов. С помощью функции стохастической чувствительности был проведен сравнительный анализ чувствительности равновесий и циклов. Опираясь на метод доверительных эллипсов получены значения интенсивности шума, при которых наблюдается переход с одного аттрактора на другой, а также формирование нового аттрактора.The paper describes a discrete time model that describes the dynamics of interaction between two consumers. Within the deterministic analysis, zone of coexistence of at least two equilibria was found. The zones of coexistence of three and more attractors were determined, and the bifurcations were described. The fractal structure of the basins of attraction were shown. The behavior of stochastic version of this model is described. The effect of additive and parametric noise on the system was studied. Using the stochastic sensitivity function, a comparative analysis of the sensitivity for equilibria and cycles was carried out. Based on the method of confidante ellipses, values of the noise intensity at which a transition from one attractor to another is observed. The formation of a new stochastic attractor was obtained

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"

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.

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