stochastic Lotka-Volterra systems

Top PDF stochastic Lotka-Volterra systems:

Global stability with selection in integro-differential Lotka-Volterra systems modelling trait-structured populations

Global stability with selection in integro-differential Lotka-Volterra systems modelling trait-structured populations

Following [ 36 ], one might consider that these two terms combine both Darwinism selection through the intrinsic growth rate r, and Lamarckism induction through the logistic death rate since it depends on the environment. Note that these models can be derived from stochastic models at the individual level [ 6 , 15 , 20 ], and more generally measure-valued functions n can be considered [ 21 ]. The asymptotic behaviour of the previous model ( 1 ) and variants is analysed in [ 19 , 25 , 31 ], and one important property among others is that solution typically tend to concentrate on a few phenotypes, a convergence to Dirac masses in mathematical terms. These models are thus successful at representing the survival of only a few phenotypes, which we will refer to as selected.
En savoir plus

26 En savoir plus

Convergence to equilibrium in competitive Lotka-Volterra and chemostat systems

Convergence to equilibrium in competitive Lotka-Volterra and chemostat systems

[10] J.A.J. Metz, S.A.H. Geritz, G. Mesz´ena, F.A.J. Jacobs, J.S. van Heer- waasden, Adaptive dynamics: a geometrical study of the consequences of nearly faithful reproduction. In S. J. van Strien and S. M. Verduyn Lunel, editors, Stochastic and Spatial Structures of Dynamical Systems, 183–231, Amsterdam, 1996.

15 En savoir plus

Lotka-Volterra with randomly fluctuating environments: a full description

Lotka-Volterra with randomly fluctuating environments: a full description

Abstract In this note, we study the long time behavior of Lotka-Volterra systems whose coeffi- cients vary randomly. Bena¨ım and Lobry established that randomly switching between two environments that are both favorable to the same species may lead to four different regimes: almost sure extinction of one of the two species, random extinction of one species or the other and persistence of both species. Our purpose here is to provide a complete description of the model. In particular, we show that any couple of environments may lead to the four different behaviours of the stochastic process depending on the jump rates.
En savoir plus

11 En savoir plus

Perturbation methods for the determination of the statistical response of nonlinear Volterra systems

Perturbation methods for the determination of the statistical response of nonlinear Volterra systems

ABSTRACT: The point-like quasi-steady aerodynamic loading in a turbulent flow is formally expressed as a function of the squared relative velocity between the fluid and the investigated structure. The three major terms governing the low-order statistics of the response are known to be related to the average loading, the linear turbulent loading and the aerodynamic damping. The three other terms in the loading, namely the quadratic turbulence term, the parametric velocity feedback term and the squared velocity term, may significantly affect the higher order statistical cumulants of the response. These latter two sources of fluid-structure interaction are usually disregarded, by lack of efficient simulation tools, except a Monte Carlo simulation of the nonlinear equation. In this paper, we provide a formal analysis of the complete nonlinear model, including thus all six terms, but mainly focusing on the importance of the two nonlinear coupling terms of the loading. Closed form solutions of the response are derived for a second-order Volterra model of this problem, under the assumption of different timescales in the loading and in the structural behavior. Two major outcomes of the analysis are, on the one hand, that the squared structural velocity term has no influence on the cumulants of the response up to order 4 and, on the other hand, that the parametric velocity feedback acts as a reduction of the non Gaussianity of the response.
En savoir plus

8 En savoir plus

Nonlinear MIMO communication systems : channel estimation and information recovery using Volterra models

Nonlinear MIMO communication systems : channel estimation and information recovery using Volterra models

The main objective of this thesis is to propose techniques for channel estima- tion and information recovery in multiple-input-multiple-output (MIMO) Volterra communication systems. This kind of MIMO model is able of modeling nonlinear communication channels with multiple transmit and receive antennas, as well as multi-user channels with a single transmit antenna for each user and multiple re- ceive antennas. Channel estimation and equalization techniques are developed for three types of nonlinear MIMO communication systems: OFDM, ROF and Code division multiple access (CDMA)-ROF systems. According to the considered com- munication systems, different kinds of MIMO Volterra models are used. In the case of OFDM systems, we develop receivers that exploit the diversity provided by a proposed transmission scheme. In the case of time and space division multiple access (TDMA-SDMA) systems, a set of orthonormal polynomials is developed for increasing the convergence speed of a supervised adaptive MIMO Volterra es- timation algorithm. Moreover, in order to develop signal processing techniques for MIMO Volterra communication channels in a blind scenario, we make use of tensor decompositions. By exploiting the fact that Volterra models are linear with respect to their coefficients, blind estimation and equalization of MIMO Volterra channels are carried out by means of the Parallel Factor (PARAFAC) tensor decomposition, considering TDMA-SDMA and CDMA communication systems.
En savoir plus

241 En savoir plus

L étude d un opérateur de Volterra

L étude d un opérateur de Volterra

Chapitre 2 OPERATEUR DE VOLTERRA On introduit dans ce chapitre un opérateur de Volterra noté V , puis à l’aide de son adjoint, on étudie alors un opérateur V V (la composition d’un opérateur de Volterra et son ad- joint) autant qu’un opérateur symétrique dé…ni positif dans un espace vectoriel euclidien de dimension in…nie en déterminant son spectre, et on relie les vecteurs propres de l’opérateur V V aux solutions d’une équation di¤érentielle. On termine ce chapitre par un théorème qui caractérise les valeurs propres de ce type d’opérateurs.
En savoir plus

39 En savoir plus

Affine Volterra processes

Affine Volterra processes

Our motivation for considering affine Volterra processes comes from applications in financial modeling. Classical affine processes arguably constitute the most popular frame- work for building tractable multi-factor models in finance. They have been used to model a vast range of risk factors such as credit and liquidity factors, inflation and other macro-economic factors, equity factors, and factors driving the evolution of interest rates; see Duffie et al. ( 2003 ) and the references therein. In particular, affine stochastic volatility models, such as the Heston ( 1993 ) model, are very popular.
En savoir plus

48 En savoir plus

Global behaviour of n-dimensional Lotka-Volterra systems

Global behaviour of n-dimensional Lotka-Volterra systems

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignemen[r]

19 En savoir plus

Affine Volterra processes

Affine Volterra processes

Our motivation for considering affine Volterra processes comes from applications in financial modeling. Classical affine processes arguably constitute the most popular frame- work for building tractable multi-factor models in finance. They have been used to model a vast range of risk factors such as credit and liquidity factors, inflation and other macro-economic factors, equity factors, and factors driving the evolution of interest rates; see Duffie et al. ( 2003 ) and the references therein. In particular, affine stochastic volatility models, such as the Heston ( 1993 ) model, are very popular.
En savoir plus

47 En savoir plus

A Formalism for Stochastic Adaptive Systems

A Formalism for Stochastic Adaptive Systems

4.2 A contract language for SAS specification The Goal and Contract Specification Language (GCSL) was first proposed in [ 2 ] to formalise properties of adaptive systems in the scope of the DANSE project. It has a strong semantics based on BLTL but it has a syntax close to the hand written English requirements. Dealing with formal temporal logic is often an issue to formalise correctly the initial English requirements. Most of the time the formalisation frequently contains some mistakes, which is due to the nesting of the temporal operators. The difficulty for correctly specifying properties is enough to make the overall methodology useless.
En savoir plus

18 En savoir plus

Accurate approximate diagnosability of stochastic systems

Accurate approximate diagnosability of stochastic systems

Keywords: automata for system analysis and programme verification 1 Introduction Diagnosis and diagnosability. The increasing use of software systems for critical operations motivates the design of fast automatic detection of malfunctions. In general, diagnosis raises two important issues: deciding whether the system is diagnosable and, in the positive case, synthesizing a diagnoser possibly satisfying additional requirements about memory size, implementability, etc. One of the proposed approaches consists in modelling these systems by partially observable labelled transition systems (LTS) [10]. In such a framework, diagnosability requires that the occurrence of unobservable faults can be deduced from the previous and subsequent observable events. Formally, an LTS is diagnosable if there exists a diagnoser that satisfies reactivity and correctness contraints. Reactivity requires that if a fault occurred, the diagnoser eventually detects it. Correctness asks that the diagnoser only claims the existence of a fault when there actually was
En savoir plus

24 En savoir plus

Stochastic Formal Methods for Hybrid Systems

Stochastic Formal Methods for Hybrid Systems

2 School of Computer Science, University of Manchester Manchester, United Kingdom M13 9PL, david.r.lesterman hester.a .uk Abstract We provide a framework to bound the probability that accumulated errors were never above a given threshold on hybrid systems. Such systems are used for example to model an aircraft or a nu- clear power plant on one side and its software on the other side. This report contains simple formulas based on Lévy’s and Markov’s inequalities and it presents a formal theory of random variables with a special focus on producing concrete results. We selected four very common applications that fit in our framework and cover the common practices of hybrid systems that evolve for a long time. We compute the number of bits that remain continuously significant in the first two applications with a probability of failure around one against a billion, where worst case analysis considers that no signif- icant bit remains. We are using PVS as such formal tools force explicit statement of all hypotheses and prevent incorrect uses of theorems.
En savoir plus

11 En savoir plus

Volterra-based Nonlinear Compensation in 400 Gb/s WDM Multiband Coherent Optical OFDM Systems

Volterra-based Nonlinear Compensation in 400 Gb/s WDM Multiband Coherent Optical OFDM Systems

This paper examines the merits of nonlinear compensation using a 3 rd -order inverse Volterra series transfer function nonlinear equalizer (IVSTF-NLE) based on a variant of the algorithm proposed in [10]. In particular, we examine whether the IVSTF-NLE performs better in a WDM, multiband, multicarrier coherent optical communication system than its most prominent counterpart, i.e., a digital back-propagation, split-step Fourier (DBP- SSF) equalizer. We show that the IVSTF-NLE provides a ~0.6 dB Q-factor improvement with respect to the purely linear equalization after 1000 km of propagation over both standard single-mode fiber (SSMF) and large effective area fiber (LEAF), while pushing the nonlinear threshold of ~1 dB. This improvement appears rather modest, due to the detection and compensation of each OFDM sub-band separately, leaving interband nonlinearities uncompensated. Nevertheless, it is superior to the one provided by the single-step-per-span DBP-SSF, which appears to be inadequate to reach the maximum efficiency of the IVSTF-NLE in the multicarrier systems under study. In addition, we show that the IVSTF-NLE can be preferable to multistep-per-span DBP-SSF in terms of computational complexity. Consequently, the IVSTF-NLE can be a reasonable choice as a first-generation nonlinear equalizer in multicarrier 400 Gb/s and 1 Tb/s systems.
En savoir plus

4 En savoir plus

Non-local Conservation Law from Stochastic Particle Systems

Non-local Conservation Law from Stochastic Particle Systems

[5] P. Biler, T. Funaki, W.A. Woyczynski, Interacting particle approximations for nonlo- cal quadratic evolution problems, Probability and Mathematical Statistics 2, 267–286 (1999). [6] V. Capasso, D. Bakstein, An introduction to continuous-time stochastic processes : theory, models, and applications to finance, biology and medicine, Series Modeling and Simulation in Science, Engineering and Technology, Birkh¨auser Basel, Springer Science+Business Media New York, 2015.

28 En savoir plus

Efficient Monte Carlo simulation of stochastic hybrid systems

Efficient Monte Carlo simulation of stochastic hybrid systems

The tool KB3, based on the Figaro modeling lan- guage, is dedicated to the construction of discrete state stochastic models, for reliability and dependa- bility calculations. With this tool it has been very easy to build a graphical model representing the heated room, using a library for hybrid stochastic Petri nets. The model was solved using the YAMS Monte Carlo simulator, able to process any Figaro model. The main concern with this approach is the impossibility to "separate" in the processing the cal- culations on the discrete and on the continuous part of the model. Thus it would probably be inefficient in terms of CPU consumption on a large model, just like the approach described in (Zhang et al. 2013), commented 15 lines below).
En savoir plus

12 En savoir plus

Analysis of primitive linear and nonlinear stochastic systems

Analysis of primitive linear and nonlinear stochastic systems

This type of research is continued here by investigating calculations of independent random variables described by uniform, gaussian, and beta distributions which arise from co[r]

92 En savoir plus

Cycle time of stochastic max-plus linear systems

Cycle time of stochastic max-plus linear systems

sequence has indices in Z, which is possible up to a change of probability space, we define a new random vector y(n, x 0 ) := A(−1, −n)x 0 , which has the same distribution as x(n, x 0 ). Sequences defined by Equation 1 model a large class of discrete event dynami- cal systems. This class includes some models of operations research like timed event graphs (F. Baccelli [ 1 ]), 1-bounded Petri nets (S. Gaubert and J. Mairesse [ 10 ]) and some queuing networks (J. Mairesse [ 15 ], B. Heidergott [ 12 ]) as well as many con- crete applications. Let us cite job-shops models (G. Cohen et al.[ 7 ]), train networks (H. Braker [ 6 ], A. de Kort and B. Heidergott [ 9 ]), computer networks (F. Baccelli and D. Hong [ 3 ]) or a statistical mechanics model (R. Griffiths [ 11 ]). For more details about modelling, see the books by F. Baccelli and al. [ 2 ] and by B. Heidergott and al. [ 13 ].
En savoir plus

18 En savoir plus

Interacting stochastic systems with individual and collective reinforcement

Interacting stochastic systems with individual and collective reinforcement

drawn in the past both in the given urn and in the whole system. Under the conditions on these probabilities, it has been shown that there is a phenomenon of fixation, i.e., depending on the strength of interaction, all or part of the urns draw eventually the same color. So, if the interaction among urns is sufficiently strong, the urns synchronize, which means that the proportion of a given color in the urns converges a.s. to the same random variable which take values in the set {0, 1}. In following section, we survey some families of interacting systems with a weaker reinforcement which are considered in various recent
En savoir plus

139 En savoir plus

Dynamic control of stochastic and fluid resource-sharing systems

Dynamic control of stochastic and fluid resource-sharing systems

In this setting we will consider three type of problems that fit the framework of optimal class selection problems: a multi-class single-server abandonment queue see Chapter 3, Section 4.[r]

356 En savoir plus

Random Walk Based Stochastic Modeling of 3D Fiber Systems

Random Walk Based Stochastic Modeling of 3D Fiber Systems

We recall in details the state-of-the-art in fiber modeling: The classical approach called dilated Poisson line process was introduced in [21] and creates infinite straight cylinders in a softcore network. Since then, the fiber modeling has evolved into more flexible approaches. In order to achieve hardcore systems, the random sequential adsorption (RSA) model was created in [28], which iteratively generates objects and tries to place them in the system, such that they do not overlap with the already existing objects. This approach was applied for cylinders in [12]. Two other random fiber packing methods have been developed: one for ellipsoids presented in [6] and one for spherocylinders in [29]. All three random packing approaches produce straight fibers in a hardcore system and achieve only low volume fractions of about 10% − 15% for isotropic orientation distribution and a fiber aspect ratio of 10. For long fibers, as it is the case for fiber reinforced composites (aspect ratio of about 200), the producible volume fraction goes down to 5%, while 15% − 55% is requested. Furthermore, long fibers cannot be realized in a periodic window, as fibers tend to overlap themselves. Still, the periodic boundary condition is often required for simulations of physical properties.
En savoir plus

16 En savoir plus

Show all 7579 documents...