Related papers: A Stochastic Differential Equation Model for Preda…
We investigate predator-prey school interactions in aquatic environments using a stochastic differential equation (SDE)-based, particle-level model that incorporates attraction, repulsion, alignment, and environmental noise. Two predation…
Stemming from the stochastic Lotka-Volterra or predator-prey equations, this work aims to model the spatial inhomogeneity by using stochastic partial differential equations (SPDEs). Compared to the classical models, the SPDE model is more…
Mathematical modeling based on time-delay differential equations is an important tool to study the role of delay in biological systems and to evaluate its impact on the asymptotic behavior of their dynamics. Delays are indeed found in many…
We present a novel model of stochastic differential equations for foraging behavior of fish schools in space including obstacles. We then study the model numerically. Three configurations of space with different locations of food resource…
This study builds upon our previously proposed stochastic differential equation (SDE)-based model to further investigate fish school fragmentation under predation. Specifically, we explore structural dynamics by incorporating…
This paper is devoted to studying obstacle avoiding patterns and cohesiveness of fish school. First, we introduce a model of stochastic differential equations (SDEs) for describing the process of fish school's obstacle avoidance. Second, on…
This note reviews our mathematical models for fish schooling, considered in free space, and in space with obstacle and food resource. These models are performed by stochastic differential equations or stochastic partial differential…
This paper presents a stochastic differential equation model for describing the process of fish schooling. The model equation always possesses a unique local solution, but global existence can be shown only in some particular cases. Some…
Experiments in predator-prey systems show the emergence of long-term cycles. Deterministic model typically fails in capturing these behaviors, which emerge from the microscopic interplay of individual based dynamics and stochastic effects.…
In this paper, preys with stochastic evasion policies are considered. The stochasticity adds unpredictable changes to the prey's path for avoiding predator's attacks. The prey's cost function is composed of two terms balancing the…
This paper investigates the long-term dynamics of a reaction-diffusion predator-prey system subject to random environmental fluctuations modeled by Markovian switching. The model is formulated as a hybrid system of partial differential…
Understanding the interaction between turbulence and zonal flows is critical for modeling turbulence transport in fusion plasmas, often described through predator-prey dynamics. However, traditional deterministic models like the…
Stochastic differential equations (SDEs) are popular tools to analyse time series data in many areas, such as mathematical finance, physics, and biology. They provide a mechanistic description of the phenomeon of interest, and their…
In this study, we apply two pillars of Scientific Machine Learning: Neural Ordinary Differential Equations (Neural ODEs) and Universal Differential Equations (UDEs) to the Lotka Volterra Predator Prey Model, a fundamental ecological model…
This paper conducts a numerical study of a geometrical structure called $\epsilon$-school for predator-avoidance fish schools, based on our previous mathematical model. Our results show that during a predator attack, the number of…
Dynamical systems are essential to model various phenomena in physics, finance, economics, and are also of current interest in machine learning. A central modeling task is investigating parameter sensitivity, whether tuning atmospheric…
There is great interest in ecology to understand how wild animals are affected by anthropogenic disturbances, such as sounds. Behavioural response studies are an important approach to quantify the impact of naval activity on marine mammals.…
We consider a broad class of stochastic lattice predator-prey models, whose main features are overviewed. In particular, this article aims at drawing a picture of the influence of spatial fluctuations, which are not accounted for by the…
The Latent Stochastic Differential Equation (SDE) is a powerful tool for time series and sequence modeling. However, training Latent SDEs typically relies on adjoint sensitivity methods, which depend on simulation and backpropagation…
We propose a stochastic lattice gas model to describe the dynamics of two animal species population, one being a predator and the other a prey. This model comprehends the mechanisms of the Lotka-Volterra model. Our analysis was performed by…