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A theoretical framework is developed for understanding the transient growth and propagation characteristics of thermodynamically coupled, meridional mode-like structures in the tropics. The model consists of a Gill-Matsuno type steady…
Recent studies have shown that deep learning (DL) models can skillfully predict the El Ni\~no-Southern Oscillation (ENSO) forecasts over 1.5 years ahead. However, concerns regarding the reliability of predictions made by DL methods persist,…
Enhancement of the predictive power and robustness of nonlinear population dynamics models allows ecologists to make more reliable forecasts about species' long term survival. However, the limited availability of detailed ecological data,…
In this paper, a novel finite - time Nonlinear Extended State Observer (NLESO) is proposed and employed in Active Disturbance Rejection Control (ADRC) to stabilize a nonlinear system against system's uncertainties and discontinuous…
A delayed term in a differential equation reflects the fact that information takes significant time to travel from one place to another within a process being studied. Despite de apparent similarity with ordinary differential equations,…
We address the propagation into an unstable state of a localised disturbance in a forward-backward diffusion pseudo-parabolic equation. Three asymptotic regimes are distinguished as t tends to infinity, the first being a regime ahead of the…
We investigate neural ordinary and stochastic differential equations (neural ODEs and SDEs) to model stochastic dynamics in fully and partially observed environments within a model-based reinforcement learning (RL) framework. Through a…
Cells and tissues exhibit oscillatory deformations during remodelling, migration or embryogenesis. Although it has been shown that these oscillations correlate with cell biochemical signalling, it is yet unclear the role of these…
The North Atlantic Oscillation (NAO) index, a measure of sea-level atmospheric pressure variability, holds significant influence over weather patterns in North America and Northern Europe. A negative (positive) NAO value signifies increased…
This paper focuses on time-varying delayed stochastic differential systems with stochastically switching parameters formulated by a unified switching behavior combining a discrete adapted process and a Cox process. Unlike prior studies…
We introduce two time-delay models of metabolic oscillations in yeast cells. Our model tests a hypothesis that the oscillations occur as multiple pathways share a limited resource which we equate to the number of available ribosomes. We…
We consider a class of dissipative stochastic differential equations (SDE's) with time-periodic coefficients in finite dimension, and the response of time-asymptotic probability measures induced by such SDE's to sufficiently regular, small…
This paper explores the exponential stability of two nonlinear wave equations coupled through their velocities. The analysis is divided into two main cases. First, we consider a system where one equation is damped, while the other…
Compartmental ordinary differential equation (ODE) models are used extensively in mathematical biology. When transit between compartments occurs at a constant rate, the well-known linear chain trick can be used to show that the ODE model is…
El Ni\~no-Southern Oscillation global (ENSO) imprint on sea surface temperature comes in many guises. To identify its tropical fingerprints and impacts on the rest of the climate system, we propose a global approach based on archetypal…
In this paper we analyze a PDE system modelling (non-isothermal) phase transitions and damage phenomena in thermoviscoelastic materials. The model is thermodynamically consistent: in particular, no {\em small perturbation assumption} is…
Dynamical systems with long delay feedback can exhibit complicated temporal phenomena, which once re-organized in a two-dimensional space are reminiscent of spatio-temporal behavior. In this framework, normal forms description have been…
Long-term fluid dynamics forecasting is a critically important problem in science and engineering. While neural operators have emerged as a promising paradigm for modeling systems governed by partial differential equations (PDEs), they…
El Ni\~no-Southern Oscillation (ENSO) exerts global climate and societal impacts, but real-time prediction with lead times beyond one year remains challenging. Dynamical models suffer from large biases and uncertainties, while deep learning…
The elapsed-time model describes the behavior of interconnected neurons through the time since their last spike. It is an age-structured non-linear equation in which age corresponds to the elapsed time since the last discharge, and models…