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
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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.
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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
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On the existence of weak solutions to stochastic Volterra equations [PDF]
Electronic Communications in Probability, 2022 The existence of weak solutions is established for stochastic Volterra equations with time-inhomogeneous coefficients allowing for general kernels in the drift and convolutional or bounded kernels in the diffusion term. The presented approach is based on
David J. Promel, David Scheffels
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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
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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
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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
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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
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Linear-quadratic control for a class of stochastic Volterra equations: Solvability and approximation [PDF]
The Annals of Applied Probability, 2019 We provide an exhaustive treatment of Linear-Quadratic control problems for a class of stochastic Volterra equations of convolution type, whose kernels are Laplace transforms of certain signed matrix measures which are not necessarily finite.
Eduardo Abi Jaber, Enzo Miller, H. Pham
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A weak solution theory for stochastic Volterra equations of convolution type [PDF]
The Annals of Applied Probability, 2019 We obtain general weak existence and stability results for stochastic convolution equations with jumps under mild regularity assumptions, allowing for non-Lipschitz coefficients and singular kernels.
Eduardo Abi Jaber +3 more
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