Bistability in a system of two species interacting through mutualism as well as competition: Chemostat vs. Lotka-Volterra equations. [PDF]
PLoS One, 2018 We theoretically study the dynamics of two interacting microbial species in the chemostat. These species are competitors for a common resource, as well as mutualists due to cross-feeding.
Vet S +5 more
europepmc +2 more sources
Food Web Assembly Rules for Generalized Lotka-Volterra Equations. [PDF]
PLoS Comput Biol, 2016 In food webs, many interacting species coexist despite the restrictions imposed by the competitive exclusion principle and apparent competition. For the generalized Lotka-Volterra equations, sustainable coexistence necessitates nonzero determinant of the
Haerter JO, Mitarai N, Sneppen K.
europepmc +2 more sources
Weak existence and uniqueness for affine stochastic Volterra equations with L1-kernels [PDF]
arXiv, 2019 We provide existence, uniqueness and stability results for affine stochastic Volterra equations with $L^1$-kernels and jumps. Such equations arise as scaling limits of branching processes in population genetics and self-exciting Hawkes processes in mathematical finance.
Eduardo Abi Jaber
arxiv +3 more sources
Volterra–Stieltjes integral equations and impulsive Volterra–Stieltjes integral equations
Electronic Journal of Qualitative Theory of Differential Equations, 2020 In this paper, we prove existence and uniqueness of solutions of Volterra–Stieltjes integral equations using the Henstock–Kurzweil integral. Also, we prove that these equations encompass impulsive Volterra–Stieltjes integral equations and prove the ...
Edgardo Alvarez +3 more
doaj +4 more sources
Generalized Lotka-Volterra Equations with Random, Nonreciprocal Interactions: The Typical Number of Equilibria. [PDF]
Physical Review Letters, 2022 We compute the typical number of equilibria of the generalized Lotka-Volterra equations describing species-rich ecosystems with random, nonreciprocal interactions using the replicated Kac-Rice method.
V. Ros +4 more
semanticscholar +1 more source
Approximation of Stochastic Volterra Equations with kernels of completely monotone type [PDF]
Mathematics of Computation, 2021 In this work, we develop a multifactor approximation for $d$-dimensional Stochastic Volterra Equations (SVE) with Lipschitz coefficients and kernels of completely monotone type that may be singular.
A. Alfonsi, Ahmed Kebaier
semanticscholar +1 more source
Markovian approximations of stochastic Volterra equations with the fractional kernel [PDF]
Quantitative finance (Print), 2021 We consider rough stochastic volatility models where the variance process satisfies a stochastic Volterra equation with the fractional kernel, as in the rough Bergomi and the rough Heston model.
Christian Bayer, Simon Breneis
semanticscholar +1 more source
Stability theory for Volterra equations
Journal of Differential Equations, 1979 T. A. Burton
openalex +3 more sources
Fractal and Fractional, 2022 This paper proposes to model fractional behaviors using Volterra equations. As fractional differentiation-based models that are commonly used to model such behaviors exhibit several drawbacks and are particular cases of Volterra equations (in the kernel ...
Vincent Tartaglione +2 more
doaj +1 more source
Classical Theory of Linear Multistep Methods for Volterra Functional Differential Equations
Discrete Dynamics in Nature and Society, 2021 Based on the linear multistep methods for ordinary differential equations (ODEs) and the canonical interpolation theory that was presented by Shoufu Li who is exactly the second author of this paper, we propose the linear multistep methods for general ...
Yunfei Li, Shoufu Li
doaj +1 more source