Related papers: Determining Parameters Leading to Chaotic Dynamics…
Ecological systems often exhibit complex nonlinear dynamics like oscillations, chaos, and regime shifts. Universal dynamic equations have shown promise in modeling complex dynamics by combining known functional forms with neural networks…
It has been proposed to make practical use of chaos in communication, in enhancing mixing in chemical processes and in spreading the spectrum of switch-mode power suppies to avoid electromagnetic interference. It is however known that for…
Due to existence of periodic windows, chaotic systems undergo numerous bifurcations as system parameters vary, rendering it hard to employ an analytic continuation, which constitutes a major obstacle for its effective analysis or…
The human microbiome is a complex ecological system, and describing its structure and function under different environmental conditions is important from both basic scientific and medical perspectives. Viewed through a biostatistical lens,…
We introduce new machine-learning techniques for analyzing chaotic dynamical systems. The primary objectives of the study include the development of a new and simple method for calculating the Lyapunov exponent using only two trajectory…
A network of $N$ elements is studied in terms of a deterministic globally coupled map which can be chaotic. There exists a range of values for the parameters of the map where the number of different macroscopic configurations is very large,…
Causal discovery for dynamical systems poses a major challenge in fields where active interventions are infeasible. Most methods used to investigate these systems and their associated benchmarks are tailored to deterministic,…
We investigate functions that are exact solutions to chaotic dynamical systems. A generalization of these functions can produce truly random numbers. For the first time, we present solutions to random maps. This allows us to check,…
There are insights of chaotic properties in economic systems and data. To prove the existence of chaotic dynamics, the establishment of a deterministic model is mandatory. A global modelling tool (GPoM) is used to search for mathematical…
The introduction of unexpected system disturbances and new system dynamics does not allow guaranteed continuous system stability. In this research we present a novel approach for detecting early failure indicators of non-linear highly…
We suggest and implement an approach for the bottom-up description of systems undergoing large-scale structural changes and chemical transformations from dynamic atomically resolved imaging data, where only partial or uncertain data on…
A fundamental requirement for the emergence of classical behavior from an underlying quantum description is that certain observed quantum systems make a transition to chaotic dynamics as their action is increased relative to $\hbar$. While…
In a smooth flow, the leading-order response of trajectories to infinitesimal perturbations in their initial conditions is described by the finite-time Lyapunov exponents and associated characteristic directions of stretching. We give a…
The possibility of complicated dynamic behaviour driven by non-linear feedbacks in dynamical systems has revolutionized science in the latter part of the last century. Yet despite examples of complicated frequency dynamics, the possibility…
In the study of chaotic behaviour of systems of many hard spheres, Lyapunov exponents of small absolute value exhibit interesting characteristics leading to speculations about connections to non-equilibrium statistical mechanics. Analytical…
An algorithm to characterize collective motion is presented, with the introduction of ``collective Lyapunov exponent'', as the orbital instability at a macroscopic level. By applying the algorithm to a globally coupled map, existence of…
The system decomposition theory has recently been developed for the dynamic analysis of nonlinear compartmental systems. The application of this theory to the ecosystem analysis has also been introduced in a separate article. Based on this…
Linearized catalytic reaction equations modeling e.g. the dynamics of genetic regulatory networks under the constraint that expression levels, i.e. molecular concentrations of nucleic material are positive, exhibit nontrivial dynamical…
We consider transitions to chaos in random dynamical systems induced by an increase of noise amplitude. We show how the emergence of chaos (indicated by a positive Lyapunov exponent) in a logistic map with bounded additive noise can be…
Dynamical chaos is a fundamental manifestation of gravity in astrophysical, many-body systems. The spectrum of Lyapunov exponents quantifies the associated exponential response to small perturbations. Analytical derivations of these…