Related papers: On the Numerical Computability of Asteroidal Lyapu…
When dealing with an orbit determination problem, uncertainties naturally arise from intrinsic errors related to observation devices and approximation models. Following the least squares method and applying approximation schemes such as the…
We calculate the maximal Lyapunov exponent in constant-energy molecular dynamics simulations at the melting transition for finite clusters of 6 to 13 particles (model rare-gas and metallic systems) as well as for bulk rare-gas solid. For…
The spacecraft attitude tracking problem is addressed with actuator faults and uncertainties among inertias, external disturbances, and, in particular, state estimates. A continuous sliding mode attitude controller is designed using…
Conditions for the emergence of a statistical relationship between $T_r$, the chaotic transport (recurrence) time, and $T_L$, the local Lyapunov time (the inverse of the numerically measured largest Lyapunov characteristic exponent), are…
Algorithms increasingly operate within complex physical, social, and engineering systems where they are exposed to disturbances, noise, and interconnections with other dynamical systems. This article extends known convergence guarantees of…
In some maps the existence of an attractor with a positive Lyapunov exponent can be proved by constructing a trapping region in phase space and an invariant expanding cone in tangent space. If this approach fails it may be possible to adapt…
We provide a computer-assisted approach to ensure that a given continuous or discrete-time polynomial system is (asymptotically) stable. Our framework relies on constructive analysis together with formally certified sums of squares Lyapunov…
We develop an extension of the fast method of angles for hyperbolicity verification in chaotic systems with an arbitrary number of time-delay feedback loops. The adopted method is based on the theory of covariant Lyapunov vectors and…
The distribution of orbital period ratios between adjacent observed exoplanets is approximately uniform, but exhibits a strong falloff toward close orbital separations. We show that this falloff can be explained through past dynamical…
Neutrino-neutrino refraction can lead to non-periodic flavor oscillations in dense neutrino gases, and it has been hypothesized that some solutions are chaotic in nature. This is of particular interest in the case of neutrino emission from…
The nervous system reorganizes memories from an early site to a late site, a commonly observed feature of learning and memory systems known as systems consolidation. Previous work has suggested learning rules by which consolidation may…
Fluids cooled to the liquid-vapor critical point develop system-spanning fluctuations in density that transform their visual appearance. Despite the rich phenomenology of this critical point, there is not currently an explanation of the…
We conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom. Chaos can be diagnosed using an out-of-time-order correlation function closely related to the commutator of…
We investigate the collective behaviour of particle orbits in the vicinity of magnetic reconnection in Earth's magneto-tail. Various regions of different kinds of orbital stability of particle motions are found. We locate regimes of…
{} {To quantify the amount of chaos that exists in the local phase space.} {A sample of orbits from four different models of the Solar neighbourhood phase space are analysed by a new chaos identification (and quantification) technique.…
This paper develops a new approach to the estimation of the degree of boundedness or stability of multidimensional nonlinear systems with time-dependent nonperiodic coefficients-an essential task in various engineering and natural science…
Detumbling refers to the act of dampening the angular velocity of the satellite. This operation is of paramount importance since it is virtually impossible to nominally perform any other operation without some degree of attitude control.…
We generate new hierarchy of many-parameter family of maps of the interval [0,1] with an invariant measure, by composition of the chaotic maps of reference [1]. Using the measure, we calculate Kolmogorov-Sinai entropy, or equivalently…
The recent paper claims that mean characteristics of chaotic orbits differ from the corresponding values averaged over the set of unstable periodic orbits, embedded in the chaotic attractor. We demonstrate that the alleged discrepancy is an…
In chaotic dynamical systems such as the weather, prediction errors grow faster in some situations than in others. Real-time knowledge about the error growth could enable strategies to adjust the modelling and forecasting infrastructure…