Real-world systems, from climate models to power grids, often fluctuate due to sensor noise, drift, or environmental variability, yet standard chaos diagnostics assume fixed parameters and asymptotic horizons. We introduce a finite-time framework for two-dimensional maps under independent, identically distributed parameter noise. First, we prove that the maximal finite-time Lyapunov exponent converges, after centering and scaling, to a Gaussian law whose mean and variance depend explicitly on the map's Jacobian statistics. Second, we develop an attractor separation algorithm that uses FTLE histograms and a geometry-based classifier to partition phase space into chaotic and periodic regions under noise. Third, we validate our theory numerically on the noisy Domenicali map, demonstrating Gaussian FTLE distributions, predictable shifts in Kaplan-Yorke dimension, and a sharp noise threshold for basin escape. Finally, we estimate the critical noise level $\sigma_c$ at which attractor coalescence occurs, using three complementary numerical methods to bound it above and to pinpoint an estimate.
Empirical entropy rates are widely used to quantify unpredictability from symbolic or time-series data, yet their interpretation is subtle in weakly chaotic dynamics, where ordinary Lyapunov exponents vanish and invariant measures are infinite. We address this issue by studying the empirical one-step conditional entrop...
We study the long-time, small-noise behavior of a class of dissipative stochastic evolution equations in a separable Hilbert space, driven by a cylindrical Wiener process whose covariance degenerates to a limiting operator in the strong operator topology. A prototypical example is a stochastic reaction-diffusion equati...
This study systematically characterize routes to chaos in finite-size random neural networks by quantifying the fraction of chaotic trajectories as a function of coupling strength and system size, providing a statistical characterization of the broad onset of chaos in finite random networks.
We investigate the stochastic stability of master--slave synchronization for a class of nonlinear dissipative PDEs with Burgers-type nonlinearity and polynomial linear operator, including the Burgers, Kuramoto--Sivashinsky, Kawahara, Benney--Lin, and Nikolaevskiy equations. Under periodic boundary conditions, each equa...
We analyze inverse stochastic resonance (ISR) in a bistable FitzHugh--Nagumo neuron driven by additive noise in the voltage variable, focusing on how neural excitability and timescale separation regulate the noise-induced modulation of spiking activity. A codimension-two bifurcation analysis identifies a narrow bistabl...
Marius E. Yamakou, Torben Krüger, H. Schulz-Baldes· 0 citations
Intermittency represents a fundamental route to chaos in nonlinear dynamical systems. In this work we introduce an adaptive control strategy in which the control parameter of an intermittent system is promoted to a dynamical variable that evolves autonomously under an auxiliary nonlinear map drawn from the same functio...
M. Yahyavi, Sina Gholizadeh, S. Behnia et al.· Physical Review Research· 5 citations
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