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Nonlinear dynamical systems with time delay are abundant in applications, but are notoriously difficult to analyse and predict because delay-induced effects strongly depend on the form of the nonlinearities involved, and on the exact way…
In this paper we propose an elementary topological approach which unifies and extends various different results concerning fixed points and periodic points for maps defined on sets homeomorphic to rectangles embedded in euclidean spaces. We…
We study the random walk of a particle in a compartmentalized environment, as realized in biological samples or solid state compounds. Each compartment is characterized by its length $L$ and the boundaries transmittance $T$. We identify two…
In this paper we study homoclinic tangles formed by transversal intersections of the stable and the unstable manifold of a {\it non-resonant, dissipative} homoclinic saddle point in periodically perturbed second order equations. We prove…
We develop in this paper a theoretical framework for the topological study of time series data. Broadly speaking, we describe geometrical and topological properties of sliding window (or time-delay) embeddings, as seen through the lens of…
We study dynamic heterogeneities in a model glass-former whose overlap with a reference configuration is constrained to a fixed value. The system phase-separates into regions of small and large overlap, so that dynamical correlations remain…
One of the most controversial hypotheses for explaining the heterogeneous dynamics of glasses postulates the temporary coexistence of two phases characterized by a high and by a low diffusivity. In this scenario, two phases with different…
Introduced as a model for hyperchaos, the generalized R"ossler system of dimension N is obtained by linearly coupling N-3 additional degrees of freedom to the original R"ossler equation. Under variation of a single control parameter, it is…
Multiple time scales in dynamical systems lead to a bundling of trajectories onto slow invariant manifolds (SIMs). Although they are absent in two-dimensional holomorphic dynamical systems, a bundling of orbits is often observed as well.…
In recent years the theory of border collision bifurcations has been developed for piecewise smooth maps that are continuous across the border, and has been successfully applied to explain nonsmooth bifurcation phenomena in physical…
Numerical bifurcation analysis, and in particular two-parameter continuation, is used in consort with numerical simulation to reveal complicated dynamics in the Mackey-Glass equation for moderate values of the delay close to the onset of…
We show how dynamical heterogeneities in glass forming systems emerge as a consequence of the existence of dynamical constraints, and we offer an interpretation of the glass transition as an entropy crisis in trajectory space (space-time)…
We propose an integral geometric approach for computing dual distributions for the parameter distributions of multilinear models. The dual distributions can be computed from, for example, the parameter distributions of conics, multiple view…
We present a mechanism for the emergence of strange attractors (observable chaos) in a two-parameter periodically-perturbed family of differential equations on the plane. The two parameters are independent and act on different ways in the…
Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…
Using bi-parametric sweeping based on symbolic representation we reveal self-similar fractal structures induced by hetero- and homoclinic bifurcations of saddle singularities in the parameter space of two systems with deterministic chaos.…
Under sufficient permanent random covalent bonding, a fluid of atoms or small molecules is transformed into an amorphous solid network. Being amorphous, local structural properties in such networks vary across the sample. A natural order…
Impacting mechanical systems with suitable parameter settings exhibit a large amplitude chaotic oscillation close to the grazing with the impacting surface. The cause behind this uncertainty is the square root singularity and the occurrence…
We study generic features of open quantum systems embedded into a continuum of scattering wavefunctions and compare them with results discussed in optics. A dynamical phase transition may appear at high level density in a many-level system…
We implement the geometric method proposed in ([9], [3], [16]) to analytically predict the sequence of bifurcations leading to a change of stability and/or the appearance of new periodic orbits in the secular 3D planetary three body…