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We perturb with an additive Gaussian white noise the Hamiltonian system associated to a cubic anharmonic oscillator. The stochastic system is assumed to start from initial conditions that guarantee the existence of a periodic solution for…
Consider a linear autonomous Hamiltonian system with a time periodic bound state solution. In this paper we study the structural instability of this bound state ^M relative to time almost periodic perturbations which are small, localized…
Non-reciprocal systems can be thought of as disobeying Newtons third law - an action does not cause an equal and opposite reaction. In recent years there has been a dramatic rise in interest towards such systems. On a fundamental level,…
In many real world chaotic systems, the interest is typically in determining when the system will behave in an extreme manner. Flooding and drought, extreme heatwaves, large earthquakes, and large drops in the stock market are examples of…
Studying the effect of mechanical perturbations on granular systems is crucial for understanding soil stability, avalanches, and earthquakes. We investigate a granular system as a laboratory proxy for fault gouge. When subjected to a slow…
The problem of flame propagation is studied as an example of unstable fronts that wrinkle on many scales. The analytic tool of pole expansion in the complex plane is employed to address the interaction of the unstable growth process with…
We describe some general results that constrain the dynamical fluctuations that can occur in non-equilibrium steady states, with a focus on molecular dynamics. That is, we consider Hamiltonian systems, coupled to external heat baths, and…
We study a one-dimensional chain of harmonically coupled units in an asymmetric anharmonic soft potential. Due to nonlinear localisation of energy, this system exhibits extreme events in the sense that individual elements of the chain show…
We introduce a new asymptotic ansatz for spherical perturbations of the Standard Model of Cosmology (SM) which applies during the $p=0$ epoch, and prove that these perturbations trigger instabilities in the SM on the scale of the supernova…
The effect of external fluctuations on the formation of spatial patterns is analysed by means of a stochastic Swift-Hohenberg model with multiplicative space-correlated noise. Numerical simulations in two dimensions show a shift of the…
I study a recently proposed statistical model of earthquake dynamics that incorporates aging as a fundamental ingredient. The model is known to generate earthquake sequences that quantitatively reproduce the spatial and temporal clustering…
Collective temporal organization in complex systems is commonly attributed to synchronization, resonance, or proximity to dynamical instabilities. Here we identify a distinct mechanism by which coherent, synchronization-like behavior can…
Topical phenomena in high-energy physics related to collision experiments of heavy nuclei ("Little Bang") and early universe cosmology ("Big Bang") involve far-from-equilibrium dynamics described by quantum field theory. One example…
Here we numerically study a model of excitable media, namely, a network with occasionally quiet nodes and connection weights that vary with activity on a short-time scale. Even in the absence of stimuli, this exhibits unstable dynamics,…
Instabilities and strong dynamical interactions between several giant planets have been proposed as a possible explanation for the surprising orbital properties of extrasolar planetary systems. In particular, dynamical instabilities would…
Motion of an ensemble of particles in a space-periodic potential well with a weak wave-like perturbation imposed is considered. We found that slow oscillations of wavenumber of the perturbation lead to occurrence of directed particle…
Deterministic chaos is commonly associated with spectral criticality: exponential sensitivity is expected when Jacobian eigenvalues exceed unity in parts of the attractor, producing the local expansion that offsets contraction elsewhere. We…
The inclusion of a fragmentation mechanism in population balance equations introduces complex interactions that make the analytical or even computational treatment much more difficult than for the pure aggregation case. This is specially…
I demonstrate that instability in a system of homogeneous scalar fields leads to the growth of super-Hubble metric perturbations. This generalizes the result that parametric resonance can lead to the growth of cosmological perturbations.…
Diffusion coefficient usually decreases when friction increases. We analyze the opposite behavior in the paradigmatic system consisting of an inertial Brownian particle moving in a symmetric spatially periodic potential and driven by an…