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Biological systems encode function not primarily in steady states, but in the structure of transient responses elicited by time-varying stimuli. Overshoots, biphasic dynamics, adaptation kinetics, fold-change detection, entrainment, and…
We explore the connection between a stochastic simulation model and an ordinary differential equations (ODEs) model of the dynamics of an excitable gene circuit that exhibits noise-induced oscillations. Near a bifurcation point in the ODE…
The evolution of particulate and multiphase systems can transition from dynamic regimes, governed by classical transport equations with well-defined damping coefficients, to anomalously slow relaxation described by rate equations when the…
This paper presents a guided tour of some specific problems encountered in the stability analysis of linear dynamical systems including delays in their systems' representation. More precisely, we will address the characterization of…
Nonlocal aggregation-diffusion models, when coupled with a spatial map, can capture cognitive and memory-based influences on animal movement and population-level patterns. In this work, we study a one-dimensional…
Coexisting periodic solutions of a dynamical system describing nonlinear optical processes of the second-order are studied. The analytical results concern both the simplified autonomous model and the extended nonautonomous model, including…
We coincidently measure the molecular frame photoelectron angular distribution and the ion sum-momentum distribution of single and double ionization of CO molecules by using circularly and elliptically polarized femtosecond laser pulses,…
We consider the scalar delay differential equation $$ \dot{x}(t)=-x(t)+f_{K}(x(t-1)) $$ with a nondecreasing feedback function $f_{K}$ depending on a parameter $K$, and we verify that a saddle-node bifurcation of periodic orbits takes place…
The utilization of multiple phosphorylation sites in regulating a biological response is ubiquitous in cell signaling. If each site contributes an additional, equivalent binding site, then one consequence of an increase in the number of…
Ordinary differential equations (ODEs) are widely used to model biological, (bio-)chemical and technical processes. The parameters of these ODEs are often estimated from experimental data using ODE-constrained optimisation. This article…
We study a model system with nematic and magnetic orders, within a channel geometry modelled by an interval, $[-D, D]$. The system is characterised by a tensor-valued nematic order parameter $\mathbf{Q}$ and a vector-valued magnetisation…
Quadratization refers to a transformation of an arbitrary system of polynomial ordinary differential equations to a system with at most quadratic right-hand side. Such a transformation unveils new variables and model structures that…
Many biological processes are supported by special molecules, called motor proteins or molecular motors, that transport cellular cargoes along linear protein filaments and can reversibly associate to their tracks. Stimulated by these…
Within the frame of an effective, coarse-grained hydrophobic-polar protein model, we employ multicanonical Monte Carlo simulations to investigate free-energy landscapes and folding channels of exemplified heteropolymer sequences, which are…
We consider the problem of deciding whether the solution sets of a parametrized polynomial system are toric in the sense that they admit a monomial parametrization. We focus on vertically parametrized systems, which are sparse systems where…
Integrating dynamical systems models with time series data is a central part of contemporary mathematical biology. With the rich variety of available models and data, numerous methods and computational tools have been developed for these…
Realistic modeling of ionic systems necessitates taking explicitly account of many-body effects. In molecular dynamics simulations, it is possible to introduce explicitly these effects through the use of additional degrees of freedom. Here…
Ordinary differential equations (ODEs) are foundational in modeling intricate dynamics across a gamut of scientific disciplines. Yet, a possibility to represent a single phenomenon through multiple ODE models, driven by different…
Nucleation is an activated process in which the system has to overcome a free energy barrier in order for a first-order phase transition between the metastable and the stable phases to take place. In the liquid-to-solid transition the…
The parameter space of dynamical systems arising in applications is often found to be high-dimensional and difficult to explore. We construct a fast algorithm to numerically analyze "quantitative features" of dynamical systems depending on…