Multiagent systems have attracted the attention of many researchers in recent years. Among them, there are the celebrated Hegselmann-Krause opinion formation model and its second-order version, the Cucker-Smale flocking model. Typically, for such systems, one is interested in investigating the asymptotic behavior of their solutions, namely the convergence to consensus for the Hegselmann-Krause...
he 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 many interesting dynamics depending on the type of interactions between neurons. We investigate the linearized stability of this equation by considering a...
Memory and delay naturally arise in mathematical models across physical scales. In molecular simulations, the generalized Langevin equation is a stochastic integro-differential equation describing a molecule (or a degree of freedom) subjected to colored (time-correlated) noise and a non-Markovian friction term~\cite{ref2,ref4}. In chemotaxis, cells respond to extracellular signals through...
Delays in feedback mechanisms are well known to generate complex behavior, including oscillations. Understanding delay effects is therefore important in fields such as biology, mathematics, economics, and engineering. Delay differential equations (DDEs) provide a natural framework for analyzing such systems, yet exact analytical solutions are rare.
We present an exact solution of a simple...
Abstract. Delay differential equations (DDEs) have become an indispensable tool in mathematical biology and the life sciences. Time delays often arise naturally in processes such as gestation, immune response, epidemiological transmission, and neural dynamics, reflecting the time lag between cause and effect. This minisymposium brings together researchers and practitioners to discuss...
