Noise Induced Phenomena in the Dynamics of Two Competing Species

Noise through its interaction with the nonlinearity of the living systems can give rise to counter-intuitive phenomena. In this paper we shortly review noise induced effects in different ecosystems, in which two populations compete for the same resources. We also present new results on spatial patterns of two populations, while modeling real distributions of anchovies and sardines. The transient dynamics of these ecosystems are analyzed through generalized Lotka-Volterra equations in the presence of multiplicative noise, which models the interaction between the species and the environment. We find noise induced phenomena such as quasi-deterministic oscillations, stochastic resonance, noise delayed extinction, and noise induced pattern formation. In addition, our theoretical results are validated with experimental findings. Specifically the results, obtained by a coupled map lattice model, well reproduce the spatial distributions of anchovies and sardines, observed in a marine ecosystem. Moreover, the experimental dynamical behavior of two competing bacterial populations in a meat product and the probability distribution at long times of one of them are well reproduced by a stochastic microbial predictive model.Comment: 23 pages, 8 figures; to be published in Math. Model. Nat. Phenom. (2016

Noise induced phenomena in ecological models

Treballs Finals de Màster en Física dels Sistemes Complexos i Biofísica, Facultat de Física, Universitat de Barcelona. Curs: 2021-2022. Tutora: M. del Carmen Miguel LópezUnderstanding population dynamics, and in particular, population cycles is one of the central issues in ecology. In this work we study noise induced phenomena in generalized Lotka-Volterra ecological models and we show how a stochastic model for population dynamics can give rise to periodic cyclic behaviour in the presence of intrinsic noise. We will show how the intrinsic noise in a prey-predator dynamics including intra-specific, or logistic auto-regulatory, interactions gives rise to a resonant frequency in the power spectrum characterizing the system evolution, but at the same time, we show that there are other types of interactions among species where a resonant frequency does not appear. Furthermore, we analyze the effects of random transport between different ecological patches or metapopulations and see that cyclic behaviours can appear, if a prey-predator dynamics is imposed, or disappea

Noise-induced phenomena in riparian vegetation dynamics

Random forcing due to the river streamflow is a key element in riparian vegetation ecosystems. It influences several aspects of the riparian landscape, the most important being the morphology and water availability. In this letter, we analytically solve a stochastic model to show how hydrological random fluctuations are able to induce both statistically stable states and bimodality in vegetation behavior. These noise-induced results can contribute to explain two well-documented features of several riparian landscapes: the bell-shaped biomass distribution along riparian transects, and spatial vegetation patchiness along a river

Stochastic attractors and noise-induced phenomena in economical dynamic models

Проект посвящен разработке математической модели стохастических аттракторов и индуцированных шумом переходов, развивает метод доверительных областей, основанный на функции стохастической чувствительности для анализа индуцированных шумом переходов и бифуркаций. Основными объектами исследования являются нелинейные модели экономической динамики (модель бизнес-циклов, модель Калдора), находящиеся под воздействием случайных возмущений различной природы и интенсивности.The project devoted to the development of mathematical models of stochastic attractors and noise-induced transitions. It develops confident domain method based on the function of stochastic sensitivity for analysis of noise-induced transitions and bifurcations. The main objects of study are the economic dynamics of nonlinear models (model of business cycles, Kaldor's model) under the influence of random perturbations of different nature and intensity.Программа развития УрФУ на 2013 год (п.2.1.1.1

Critical Transitions in financial models: Bifurcation- and noise-induced phenomena

A so-called Critical Transition occurs when a small change in the input of a system leads to a large and rapid response. One class of Critical Transitions can be related to the phenomenon known in the theory of dynamical systems as a bifurcation, where a small parameter perturbation leads to a change in the set of attractors of the system. Another class of Critical Transitions are those induced by noisy increments, where the system switches randomly between coexisting attractors. In this thesis we study bifurcation- and noise-induced Critical Transitions applied to a variety of models in finance and economy. Firstly, we focus on a simple model for the bubbles and crashes observed in stock prices. The bubbles appear for certain values of the sensitivity of the price based on past prices, however, not always as a Critical Transition. Incorporating noise to the system gives rise to additional log-periodic structures which precede a crash. Based on the centre manifold theory we introduce a method for predicting when a bubble in this system can collapse. The second part of this thesis discusses traders' opinion dynamics captured by a recent model which is designed as an extension of a mean-field Ising model. It turns out that for a particular strength of contrarian attitudes, the traders behave chaotically. We present several scenarios of transitions through bifurcation curves giving the scenarios a market interpretation. Lastly, we propose a dynamical model where noise-induced transitions in a double-well potential stand for a company shifting from a healthy state to a defaulted state. The model aims to simulate a simple economy with multiple interconnected companies. We introduce several ways to model the coupling between agents and compare one of the introduced models with an already existing doubly-stochastic model. The main objective is to capture joint defaults of companies in a continuous-time dynamical system and to build a framework for further studies on systemic and individual risk

External noise-induced phenomena in CO oxidation on single crystal surfaces

7 pages, 6 figures.-- PACS 81.65.Mq, 82.65.+r, 82.20.-w, 82.30.-bThe influence of external noise on minimalistic models for the catalytic CO oxidation on Ir(111) and Pt(111) is studied by means of the adiabatic elimination technique. Two models, which reproduce the bistable behavior usually observed in CO oxidation on Pt group metal surfaces, are analyzed. The noise is superposed on the fraction of CO in the constant gas flow directed at the surfaces and the resulting stochastic systems are reduced after the adiabatic elimination of oxygen coverage. This reduction allows us to analyze theoretically the interplay between external noise and the kinetic bistability of CO oxidation. We report the phenomena of noise-induced shifts of steady states and noise-induced jumps between stable steady states. We also present evidence for noise-induced transitions from mono- to bistability. The theoretical results are compared with simulations of the original two-variable stochastic reaction systems.We acknowledge the financial support of Project No. FIS2007-60327 from MICINN (Spain) and FEDER (EU)Peer reviewe

Multimodal stationary states under Cauchy noise

A L\'evy noise is an efficient description of out-of-equilibrium systems. The presence of L\'evy flights results in a plenitude of noise-induced phenomena. Among others, L\'evy flights can produce stationary states with more than one modal value in single-well potentials. Here, we explore stationary states in special double-well potentials demonstrating that a sufficiently high potential barrier separating potential wells can produce bimodal stationary states in each potential well. Furthermore, we explore how the decrease in the barrier height affects the multimodality of stationary states. Finally, we explore a role of the multimodality of stationary states on the noise induced escape over the static potential barrier.Comment: 10 pages, 11 figure