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Conceptual climate models provide an approach to understanding climate processes through a mathematical analysis of an approximation to reality. Recently, these models have also provided interesting examples of nonsmooth dynamical systems.…
Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. During the last years, intensive efforts…
When the Poincar\'{e} map associated with a periodic orbit of a hybrid dynamical system has constant-rank iterates, we demonstrate the existence of a constant-dimensional invariant subsystem near the orbit which attracts all nearby…
An estimate on the number of distinct relative periodic orbits around a stable relative equilibrium in a Hamiltonian system with continuous symmetry is given. This result constitutes a generalization to the Hamiltonian symmetric framework…
The dynamics of any spherical cosmology with a scalar field (`scalaron') coupling to gravity is described by the nonlinear second-order differential equations for two metric functions and the scalaron depending on the `time' parameter. The…
Limits and characteristic periods of variations in orbital elements of planets were studied by numerical integration of equations of motion. Interrelations between the characteristic periods of variations in orbital elements of some planets…
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
Many exo-solar systems discovered in the last decade consist of planets orbiting in resonant configurations and consequently, their evolution should show long-term stability. However, due to the mutual planetary interactions a multi-planet…
We show that, near periodic orbits, a class of hybrid models can be reduced to or approximated by smooth continuous-time dynamical systems. Specifically, near an exponentially stable periodic orbit undergoing isolated transitions in a…
In Hamiltonian systems subjected to periodic perturbations the stable and unstable manifolds of the unstable periodic orbits provide the dynamical "skeleton" that drives the mixing process and bounds the chaotic regions of the phase space.…
The topology of complex classical paths is investigated to discuss quantum tunnelling splittings in one-dimensional systems. Here the Hamiltonian is assumed to be given as polynomial functions, so the fundamental group for the Riemann…
It is known that in Friedmann-Lemaitre-Robertson-Walker cosmology one has more number of dynamical equations, compared to the number of unknown variables. This fact makes some equations redundant. The situation becomes complicated because…
We obtain improved local well-posedness results for the Lorentzian timelike minimal surface equation. In dimension $d=3$, for a surface of arbitrary co-dimension, we show a gain of $1/3$ derivative regularity compared to a generic equation…
This work explores the dynamic properties of test particles surrounding a distorted, deformed compact object. The astrophysical motivation was to choose such background, which could constitute a more reasonable model of a real situation…
The small angle approximation often fails to explain experimental data, does not even predict if a plane pendulum's period increases or decreases with increasing amplitude. We make a perturbation ansatz for the Conserved Energy Surfaces of…
We consider the dynamics of complex rational maps on the Riemann sphere. We prove that, after reducing their orbits to a fixed number of positive values representing the Fubini-Study distances between finitely many initial elements of the…
Complex systems are characterized by specific time-dependent interactions among their many constituents. As a consequence they often manifest rich, non-trivial and unexpected behavior. Examples arise both in the physical and non-physical…
We present an explicit multiscale algorithm for solving differential equations for problems with high-frequency modes that can be averaged over by separating and scaling the fast and slow dynamics within a single equation. We introduce a…
We propose a novel method for fast and scalable evaluation of periodic solutions of systems of ordinary differential equations for a given set of parameter values and initial conditions. The equations governing the system dynamics are…
The dynamics of the delay logistic equation with complex parameters and arbitrary complex initial conditions is investigated. The analysis of the local stability of this difference equation has been carried out. We further exhibit several…