Related Experiment Video
Updated: May 11, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
Published on: September 23, 2025
Discontinuous attractor dimension at the synchronization transition of time-delayed chaotic systems
Steffen Zeeb1, Thomas Dahms, Valentin Flunkert
1Institute of Theoretical Physics, University of Würzburg, Am Hubland, D-97074 Würzburg, Germany. steffen.zeeb@physik.uni-wuerzburg.de
Abstract:
The attractor dimension at the transition to complete synchronization in a network of chaotic units with time-delayed couplings is investigated. In particular, we determine the Kaplan-Yorke dimension from the spectrum of Lyapunov exponents for iterated maps and for two coupled semiconductor lasers. We argue that the Kaplan-Yorke dimension must be discontinuous at the transition and compare it to the correlation dimension. For a system of Bernoulli maps, we indeed find a jump in the correlation dimension. The magnitude of the discontinuity in the Kaplan-Yorke dimension is calculated for networks of Bernoulli units as a function of the network size. Furthermore, the scaling of the Kaplan-Yorke dimension as well as of the Kolmogorov entropy with system size and time delay is investigated.
Related Concept Videos
Classification of Systems-II
Limits with Oscillating Discontinuities
Stability
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...
BIBO stability of continuous and discrete -time systems
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.
Linear time-invariant Systems
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be calculated...
State Space Representation
Consider an RLC circuit, a...
