Related papers: Canards, folded nodes and mixed-mode oscillations …
We study the solutions of a friction oscillator subject to stiction. This discontinuous model is non-Filippov, and the concept of Filippov solution cannot be used. Furthermore some Carath\'eodory solutions are unphysical. Therefore we…
We investigate the role of topological methods in the analysis of canard-type periodic and chaotic trajectories. In the first part of the paper, we apply topological degree to the analysis of multi-dimensional canards. The second part is…
Neural mass models are ubiquitous in large scale brain modelling. At the node level they are written in terms of a set of ODEs with a nonlinearity that is typically a sigmoidal shape. Using structural data from brain atlases they may be…
We report a detailed analysis on the emergence of bursting in a recently developed neural mass model that takes short-term synaptic plasticity into account. The one being used here is particularly important, as it represents an exact…
We discuss the nonlinear dynamics and fluctuations of interfaces with bending rigidity under the competing attractions of two walls with arbitrary permeabilities. This system mimics the dynamics of confined membranes. We use a two-dimension…
Synchronization phenomena in complex systems are fundamental to understanding collective behavior across disciplines. While classical approaches model such systems by using scalar-weighted networks and simple diffusive couplings, many…
We investigate a variational Monte Carlo framework for trapped one-dimensional mixture of spin-$\frac{1}{2}$ fermions using Kolmogorov-Arnold networks (KANs) to construct universal neural-network wavefunction ans\"atze. The method can, in…
Sub-pixel matching of multimodal optical images is a critical step in combined application of multiple sensors. However structural noise and inconsistencies arising from variations in multimodal image responses usually limit the accuracy of…
In this paper, we use geometric singular perturbation theory and blowup, as our main technical tool, to study the mixed-mode oscillations (MMOs) that occur in two coupled FitzHugh-Nagumo units with symmetric and repulsive coupling. In…
Slow-fast dynamical systems, i.e., singularly or non-singularly perturbed dynamical systems possess slow invariant manifolds on which trajectories evolve slowly. Since the last century various methods have been developed for approximating…
A sudden transition to a state of high amplitude limit cycle oscillations is catastrophic in a thermo-fluid system. Conventionally, upon varying the control parameter, a sudden transition is observed as an abrupt jump in the amplitude of…
Multi-hybrid architectures are poised to take over language modeling due to better quality and performance. We introduce a hierarchical decomposition framework for linear recurrences that allows us to develop algorithms aligned with GPU…
The dynamics of complex systems generally include high-dimensional, non-stationary and non-linear behavior, all of which pose fundamental challenges to quantitative understanding. To address these difficulties we detail a new approach based…
We study a class of multi-parameter three-dimensional systems of ordinary differential equations that exhibit dynamics on three distinct timescales. We apply geometric singular perturbation theory to explore the dependence of the geometry…
Phase control of parametric modulation in coupled oscillator networks enables sculpting of dynamical states with desired spatiotemporal symmetries. Symmetry-aware Floquet analysis successfully predicts such states in linear systems, but…
Entanglement between large numbers of quantum modes is the quintessential resource for future technologies such as the quantum internet. Conventionally the generation of multimode entanglement in optics requires complex layouts of…
In this paper we present a systematic, data-driven approach to discovering "bespoke" coarse variables based on manifold learning algorithms. We illustrate this methodology with the classic Kuramoto phase oscillator model, and demonstrate…
Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial…
Many natural and technological systems fail to adapt to changing external conditions and move to a different state if the conditions vary too fast. Such "non-adiabatic" processes are ubiquitous, but little understood. We identify these…
In this article, we study the Brusselator partial differential equation (PDE) in the limit in which the diffusivity of the activator is much smaller than that of the inhibitor. The PDE robustly exhibits a subcritical Turing bifurcation…