Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2609.32735

Characterization and Monitoring of Nonlinear Dynamics and Chaos in Complex Physiological Systems

Hui Yang·Yun Chen·Fabio Leonelli
View original source ↗Read source document ↗Export metadata ↓

Abstract

Nonlinear dynamics arise whenever multifarious entities of a system cooperate, compete, or interfere. For example, cardiovascular system involves a great level of complexity. Multi-lead ECG signals are generated through orchestrated depolarization and repolarization of cells and manifest significant nonlinear dynamics. Nonlinear dynamical systems defy understanding based on the traditional reductionist's approach, in which one attempts to understand a system's behavior by combining all constituent parts that have been analyzed separately. In order to cope with system complexity, modern healthcare systems are investing in advanced physiological sensing and patient monitoring, thereby giving rise to big data. Realizing the full potential of big data for healthcare intelligence requires fundamentally new methodologies to harness and exploit complexity. However, available nonlinear dynamics techniques are either not concerned with healthcare analytical objectives or fail to effectively analyze big data to extract useful information for improving healthcare services. There is an urgent need to develop analytical methodologies that fully exploit the underlying nonlinear dynamics in physiological systems for advancing healthcare services with exceptional features such as personalization, responsiveness, and superior quality. This chapter presents some theoretical developments and tools to advance the applications of nonlinear dynamics principles in health care. Specifically, we focus on sensor-based characterization and modeling of nonlinear dynamics (i.e., multifractal analysis and multiscale recurrence quantification). Then, current developments and applications of these methodologies are examined for characterizing and exploiting heart rate variability and space-time ECG signals.

Explore related subjects

eess.SYcs.SYstat.AP

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Hui Yang, Yun Chen, Fabio Leonelli. 2026-09-26. Characterization and Monitoring of Nonlinear Dynamics and Chaos in Complex Physiological Systems. https://doi.org/10.1002/9781118919408.ch3

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

KEEP EXPLORING

Related papers

arXiv2026

Output-Positive Adaptive Control of Parabolic PDE-ODE Cascades

In this paper, we propose a safe adaptive boundary control strategy for a class of parabolic partial differential equation-ordinary differential equation (PDE-ODE) cascaded systems with parametric uncertainties in both the PDE and ODE subsystems. The proposed design is built upon an adaptive Control Barrier Function (aCBF) framework that incorporates high-relative-degree CBFs together with a batch least-squares identification (BaLSI)-based adaptive control that guarantees exact parameter identification in finite time. The proposed controller ensures the positivity, i.e., the safety, of the plant output state that is the furthest state from the control input, as well as the exponential regulation of the overall plant state to zero. Numerical simulations are provided to demonstrate the effectiveness of the proposed approach.

eess.SY↗
arXiv2026

Grid-ECO: Grid Aware Electric Vehicle Charging Stations Placement Optimizer

We develop Grid-ECO, a method for optimally allocating electric vehicle charging stations (EVCS) within a distribution feeder while accounting for EV charging demand at census-level granularity. The underlying problem is a mixed-integer bilinear program (MIBLP) and requires satisfying nonlinear, nonconvex, three-phase unbalanced AC network constraints while including integer siting and sizing decision variables. Existing works cannot guarantee AC feasibility or optimality without either i) relaxing the integer decision variable space or ii) convexifying AC constraints. Grid-ECO solves the exact MIBLP to near-zero optimality gap while prioritizing candidate charging locations using grid voltage and current sensitivity metrics. To solve the MIBLP exactly, we leverage the global optimization algorithm: spatial branch-and-bound (sBnB). To scale the approach to large-scale feeders, we develop a presolving routine that combines i) a penalty-based NLP heuristic for warm-start with b) a sequential bound tightening (SBT) algorithm to derive tight bounds on both bilinear and lifted McCormick variables. Case studies using realistic Seattle city data demonstrate that Grid-ECO substantially outperforms an off-the-shelf commercial sBnB solver. In three of the four test cases, the commercial solver failed to identify a feasible solution or certify optimality within the 12-hour time limit, whereas Grid-ECO solved all instances to a reported optimality gap of 0.00%, with a maximum solver time of 753s. The results further show that tightening both bilinear and lifted McCormick variables reduces sBnB node exploration by up to 98% and solution time by up to 69%, while preserving AC-feasible solutions across all test cases.

eess.SY↗
arXiv2026

SCORE: Statistical Certification of Regions of Attraction via Extreme Value Theory

Certifying the Region of Attraction (ROA) for high-dimensional nonlinear dynamical systems remains a severe computational bottleneck. Traditional deterministic verification methods provide hard guarantees but suffer from the curse of dimensionality, typically failing to scale beyond 20 dimensions. To overcome these limitations, we propose SCORE, a statistical certification framework that shifts from seeking deterministic guarantees to bounding the worst-case safety violation with high statistical confidence. By integrating Projected Stochastic Gradient Langevin Dynamics (PSGLD) with Extreme Value Theory (EVT), we frame ROA certification as a constrained extreme-value estimation problem. Under stationary sampling and a regular local-geometry condition around the global maximum, we show that the Lyapunov derivative belongs to the Weibull maximum domain of attraction. Its finite right endpoint enables statistical estimation of the global maximum of the Lyapunov derivative and construction of an upper confidence bound, conditional on the sampling and inference assumptions. Numerical experiments validate that our EVT-based approach achieves certification tightness competitive to exact Sum of Squares programming on a 2D Van der Pol benchmark. Furthermore, we demonstrate strong scalability by successfully applying the statistical verification procedure to a dense, unstructured 500-dimensional ODE system at a nominal confidence level of 99.99\%, effectively bypassing the severe combinatorial constraints that limit existing formal verification pipelines.

eess.SY↗