Related papers: Synchronized Memory-Dependent Intracellular Oscill…
We analyze a class of cell-bulk coupled PDE-ODE models, motivated by quorum and diffusion sensing phenomena in microbial systems, that characterize communication between localized spatially segregated dynamically active signaling…
We analyze oscillatory instabilities for a coupled PDE-ODE system modeling the communication between localized spatially segregated dynamically active signaling compartments that are coupled through a passive extracellular bulk diffusion…
A class of coupled cell-bulk ODE-PDE models is formulated and analyzed in a two-dimensional domain, which is relevant to studying quorum sensing behavior on thin substrates. In this model, spatially segregated dynamically active signaling…
In this paper, we investigate how the self-synchronization property of a swarm of Kuramoto oscillators can be controlled and exploited to achieve target densities and target phase coherence. In the limit of an infinite number of…
We study the dynamics of systems consisting of two spatially segregated ODE compartments coupled through a one-dimensional bulk diffusion field. For this coupled PDE-ODE system, we first employ a multi-scale asymptotic expansion to derive…
We present a model of systems of cells with intracellular oscillators (`clocks'). This is motivated by examples from developmental biology and from the behavior of organisms on the threshold to multicellularity. Cells undergo random motion…
The neural ordinary differential equation (ODE) framework has emerged as a powerful tool for developing accelerated surrogate models of complex physical systems governed by partial differential equations (PDEs). A popular approach for PDE…
Reaction-diffusion systems have been widely used to study spatio-temporal phenomena in cell biology, such as cell polarization. Coupled bulk-surface models naturally include compartmentalization of cytosolic and membrane-bound polarity…
Spatiotemporal neural dynamics and oscillatory synchronization are widely implicated in biological information processing and have been hypothesized to support flexible coordination such as feature binding. By contrast, most deep learning…
Systems of mobile physical entities exchanging information with their neighborhood can be found in many different situations. The understanding of their emergent cooperative behaviour has become an important issue across disciplines,…
Spontaneous synchronization is a remarkable collective effect observed in nature, whereby a population of oscillating units, which have diverse natural frequencies and are in weak interaction with one another, evolves to spontaneously…
For a 2-D coupled PDE-ODE bulk-cell model, we investigate symmetry-breaking bifurcations that can emerge when two bulk diffusing species are coupled to two-component nonlinear intracellular reactions that are restricted to occur only within…
In the context of the celebrated Kuramoto model of globally-coupled phase oscillators of distributed natural frequencies, which serves as a paradigm to investigate spontaneous collective synchronization in many-body interacting systems, we…
We analyze two classes of Kuramoto models on spheres that have been introduced in previous studies. Our analysis is restricted to ensembles of identical oscillators with the global coupling. In such a setup, with an additional assumption…
A parallel program together with the parallel hardware it is running on is not only a vehicle to solve numerical problems, it is also a complex system with interesting dynamical behavior: resynchronization and desynchronization of parallel…
In this work we analyse a PDE-ODE problem modelling the evolution of a Glioblastoma, which includes an anisotropic nonlinear diffusion term with a diffusion velocity increasing with respect to vasculature. First, we prove the existence of…
A fundamental understanding of synchronized behavior in multi-agent systems can be acquired by studying analytically tractable Kuramoto models. However, such models typically diverge from many real systems whose dynamics evolve under…
In this paper, we investigate the mean-field optimal control problem of a swarm of Kuramoto oscillators. Using the notion of wrapped distribution, we explain the connection between the stochastic particle system and the mean-field PDE on…
Kuramoto model is one of the most prominent models for the synchronization of coupled oscillators. It has long been a research hotspot to understand how natural frequencies, the interaction between oscillators, and network topology…
We explore both analytically and numerically an ensemble of coupled phase-oscillators governed by a Kuramoto-type system of differential equations. However, we have included the effects of time-delay (due to finite signal-propagation…