Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1611.03403

Synergistic Dynamic Theory of Complex Coevolutionary Systems: Disentangling Nonlinear Spatiotemporal Controls on Precipitation

Rui A. P. Perdigão·Carlos A. L. Pires·Julia Hall
View original source ↗Read source document ↗Export metadata ↓

Abstract

We formulate a nonlinear synergistic theory of coevolutionary systems, disentangling and explaining dynamic complexity in terms of fundamental processes for optimised data analysis and dynamic model design: Dynamic Source Analysis (DSA). DSA provides a nonlinear dynamical basis for spatiotemporal datasets or dynamical models, eliminating redundancies and expressing the system in terms of the smallest number of fundamental processes and interactions without loss of information. This optimises model design in dynamical systems, expressing complex coevolution in simple synergistic terms, yielding physically meaningful spatial and temporal structures. These are extracted by spatiotemporal decomposition of nonlinearly interacting subspaces via the novel concept of a Spatiotemporal Coevolution Manifold. Physical consistency is ensured and mathematical ambiguities are avoided with fundamental principles on energy minimisation and entropy production. The relevance of DSA is illustrated by retrieving a non-redundant, synergistic set of nonlinear geophysical processes exerting control over precipitation in space and time over the Euro-Atlantic region. For that purpose, a nonlinear spatiotemporal basis is extracted from geopotential data fields, yielding two independent dynamic sources dominated respectively by meridional and zonal circulation gradients. These sources are decomposed into spatial and temporal structures corresponding to multiscale climate dynamics. The added value of nonlinear predictability is brought out in the geospatial evaluation and dynamic simulation of evolving precipitation distributions from the geophysical controls, using DSA-driven model building and implementation. The simulated precipitation is found to be in agreement with observational data, which they not only describe but also dynamically link and attribute in synergistic terms of the retrieved dynamic sources.

Explore related subjects

math.DSphysics.ao-ph

Keep this discovery

BibTeXRIS

Rui A. P. Perdigão, Carlos A. L. Pires, Julia Hall. 2016-11-10. Synergistic Dynamic Theory of Complex Coevolutionary Systems: Disentangling Nonlinear Spatiotemporal Controls on Precipitation. https://arxiv.org/abs/1611.03403

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Admissible Fourier Lengths, KAM Reducibility, and Spectral Applications

We develop a perturbative KAM reducibility theory for one-frequency $\mathrm{SL}(2,\mathbb{R})$ cocycles based on an admissible Fourier length $\ell$. The regularity relevant to the iteration is measured by positive adapted Fourier width rather than ordinary smoothness in the Euclidean length $|n|$. The same length governs Fourier decay, truncation and resonance scales, and the arithmetic condition controlling the small divisors. This framework contains the classical analytic and Gevrey settings, while non-monotone choices of $\ell$ allow classical nowhere differentiable Weierstrass-type perturbations and continuous perturbations outside every positive H\"older class. As spectral applications, we obtain purely absolutely continuous spectrum for every phase and $1/2$-H\"older continuity of the integrated density of states for the associated quasiperiodic Schr\"odinger operators. The Aubry dual has pure point spectrum for Lebesgue almost every dual phase, with eigenfunctions exponentially localized in the metric induced by $\ell$. We also construct nowhere differentiable quasiperiodic potentials with purely absolutely continuous Cantor spectrum.

math.DS↗
arXiv2026

Dynamics inside the attracting basins of some skew products

Polynomial skew products in $\mathbb{C}^2$ are maps of the form $F(z,w)=(P(z),Q(z,w))$, where $P$ and $Q$ are polynomials. Their local dynamics have been widely investigated. In this paper, we study the global dynamics inside Fatou components of some skew products. We consider all the inverse images in a Fatou component of a given point and use the Kobayashi metric to measure the distance between points. In the cases we consider, there are always arbitrarily large Kobayashi balls in the complement of these inverse sets.

math.DS↗
arXiv2026

Ergodicity of dynamical systems without uniqueness of orbits

Recently, there has been considerable interest in the study of non-deterministic dynamical systems. To analyze the chaotic behavior of such systems from a measure-theoretic viewpoint, it is desirable to consider ergodicity. However, the classical definition of ergodicity involves invariant sets, whose definition is not unique for non-deterministic dynamical systems. Thus, we are led to the question of which invariance yields an interesting definition of ergodicity. Here, we propose a definition based on the strong backward invariance and show that analogs of classical results hold. We also consider implications of the Birkhoff ergodic theorem for systems without uniqueness of orbits.

math.DS↗