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In order to describe excitable reaction-diffusion systems, we derive a two-dimensional model with a Hopf and a semilocal saddle-node homoclinic bifurcation. This model gives the theoretical framework for the analysis of the saddle-node…
In a recent feature article in this journal, co-authored by Gert van der Heijden, I described the static-dynamic analogy and its role in understanding the localized post-buckling of shell-like structures, looking exclusively at integrable…
Motivated by observations of snap-through phenomena in buckled elastic strips subject to clamping and lateral end translations, we experimentally explore the multi-stability and bifurcations of thin bands of various widths and compare these…
We investigate the pattern dynamics of the one-dimensional nonreciprocal Swift-Hohenberg model. Characteristic spatiotemporal patterns such as disordered, aligned, swap, chiral-swap, and chiral phases emerge depending on the parameters. We…
Active filaments, such as microtubules with attached cargo-carrying motor proteins, are important dynamic structures for fluid transport in and around living cells. The mathematical models of active filaments appearing in the literature…
The main objective of this article is to study the dynamics of the stratified rotating Boussinesq equations, which are a basic model in geophysical fluid dynamics. First, for the case where the Prandtl number is greater than one, a complete…
We study a model for a dilute suspension of rod-like particles swimming at constant velocity in a Stokes flow. As the translational diffusivity of the particles decreases, a two-dimensional uniform concentration of randomly aligned…
Varying one of the governing parameters of a dynamical system may lead to a critical transition, where the new stable state is undesirable. In some cases, there is only a limited range of the bifurcation parameter that corresponds to that…
The equilibrium configuration of an engineering structure, able to withstand a certain loading condition, is usually associated with a local minimum of the underlying potential energy. However, in the nonlinear context, there may be other…
Many elastic structures exhibit rapid shape transitions between two possible equilibrium states: umbrellas become inverted in strong wind and hopper popper toys jump when turned inside-out. This snap-through is a general motif for the…
We find and characterize an excitability regime mediated by localized structures in a dissipative nonlinear optical cavity. The scenario is that stable localized structures exhibit a Hopf bifurcation to self-pulsating behavior, that is…
The interplay between activity and elasticity often found in active and living systems triggers a plethora of autonomous behaviors ranging from self-assembly and collective motion to actuation. Amongst these, spontaneous self-oscillations…
The interplay between bifurcations and random switching processes of vector fields is studied. More precisely, we provide a classification of piecewise deterministic Markov processes arising from stochastic switching dynamics near fold,…
The dynamics of a model, originally proposed for a type of instability in plastic flow, has been investigated in detail. The bifurcation portrait of the system in two physically relevant parameters exhibits a rich variety of dynamical…
We study the semiclassical limit of the anisotropic two-photon Dicke model with a dissipative bosonic field and describe its rich nonlinear dynamics. Besides normal and 'superradiant'-like phases, the presence of localized fixed points…
The modeling of the beating of cilia and flagella in fluids is a particularly active field of study, given the biological relevance of these organelles. Various mathematical models have been proposed to represent the nonlinear dynamics of…
We propose a topological framework for the detection of Hopf bifurcations directly from time series, based on persistent homology applied to phase space reconstructions via Takens embedding within the framework of Topological Data Analysis.…
The accurate mathematical modeling of droplet impact dynamics on micro-structured surfaces is fundamental to understanding and predicting complex fluid behaviors relevant to a wide range of engineering and scientific applications. In…
We study the dynamics arising when two identical oscillators are coupled near a Hopf bifurcation where we assume a parameter $\epsilon$ uncouples the system at $\epsilon=0$. Using a normal form for $N=2$ identical systems undergoing Hopf…
A nonlinear dynamical system model that approximates a microscopic Gibbs field model for the yielding of a viscoplastic material subjected to varying external stress recently reported in [1] is presented. The predictions of the model are in…