Related papers: An economic cross-diffusion mutualistic model for …
The recovery of society after a large scale disaster generally consists of two phases, short- and long-term recoveries. The problem of short-term recovery is rather close to the problem of resilience in their goal, namely, bouncing the…
Understanding how patterns and travelling waves form in chemical and biological reaction-diffusion models is an area which has been widely researched, yet is still experiencing fast development. Surprisingly enough, we still do not have a…
In this paper we consider a class of stochastic reaction-diffusion equations. We provide local well-posedness, regularity, blow-up criteria and positivity of solutions. The key novelties of this work are related to the use transport noise,…
A mutualist model with nonlocal diffusions and a free boundary is first considered. We prove that this problem has a unique solution defined $t\ge0$, and its dynamics are governed by a spreading-vanishing dichotomy. Some criteria for…
We consider a modified Lotka-Volterra model applied to the predator-prey system that can also be applied to other areas, for instance the bank system. We show that the model is well-posed (non-negativity of solutions and conservation law)…
The ubiquitous existence of microbial communities marks the importance of understanding how species interact within the community to coexist and their spatial organization. We study a two-species mutualistic cross-feeding model through a…
Our computational economic analysis investigates the relationship between inequality, mobility and the financial accumulation process. Extending the baseline model by Levy et al., we characterise the economic process through stylised return…
We analyze a reaction-diffusion system describing the growth of microbial species in a model of flocculation type that arises in biology. Existence of global classical positive solutions is proved under general growth assumptions, with…
We present several models to describe the stochastic evolution of stocks that show some strong resistance at some level and generalize to this situation the evolution based upon geometric Brownian motion. If volatility and drift are related…
It is well-established that including spatial structure and stochastic noise in models for predator-prey interactions invalidates the classical deterministic Lotka-Volterra picture of neutral population cycles. In contrast, stochastic…
This article is concerned with a mutualism ecological model with stochastic perturbations. the local existence and uniqueness of a positive solution are obtained with positive initial value, and the asymptotic behavior to the problem is…
We study the continuous time portfolio optimization model on the market where the mean returns of individual securities or asset categories are linearly dependent on underlying economic factors. We introduce the functional $Q_\gamma$…
We investigate spatially inhomogeneous versions of the stochastic Lotka-Volterra model for predator-prey competition and coexistence by means of Monte Carlo simulations on a two-dimensional lattice with periodic boundary conditions. To…
A class of parabolic cross-diffusion systems modeling the interaction of an arbitrary number of population species is analyzed in a bounded domain with no-flux boundary conditions. The equations are formally derived from a random-walk…
We study the stochastic spatial Lotka-Volterra (LV) model for predator-prey interaction subject to a periodically varying carrying capacity. The LV model with on-site lattice occupation restrictions that represent finite food resources for…
The ongoing rapid urbanization phenomena make the understanding of the evolution of urban environments of utmost importance to improve the well-being and steer societies towards better futures. Many studies have focused on the emerging…
Populations of competing biological species exhibit a fascinating interplay between the nonlinear dynamics of evolutionary selection forces and random fluctuations arising from the stochastic nature of the interactions. The processes…
We propose a kinetic model to describe the dynamical evolution of wealth and knowledge in national and global markets, starting from a microscopic description of individual interactions. The model is built upon interaction rules that…
Although the cooperative dynamics emerging from a network of interacting players has been exhaustively investigated, it is not yet fully understood when and how network reciprocity drives cooperation transitions. In this work, we…
This work introduces a new framework for modeling financial markets through an interpretable probabilistic state machine. By clustering historical returns based on momentum and risk features across multiple time horizons, we identify…