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Nonlinear dynamical systems subjected to a combination of noise and time-varying forcing can exhibit sudden changes, critical transitions or tipping points where large or rapid dynamic effects arise from changes in a parameter that are…

The transient behavior of an ecosystem with N random interacting species in the presence of a multiplicative noise is analyzed. The multiplicative noise mimics the interaction with the environment. We investigate different asymptotic…

Low-order frequency response models for power systems have a decades-long history in optimization and control problems such as unit commitment, economic dispatch, and wide-area control. With a few exceptions, these models are built upon the…

The effect of noise is studied in one-dimensional maps undergoing transcritical, tangent, and pitchfork bifurcations. The attractors of the noiseless map become metastable states in the presence of noise. In the weak-noise limit, a…

We analyze the effects of noise on the permutation entropy of dynamical systems. We take as numerical examples the logistic map and the R\"ossler system. Upon varying the noise strengthfaster, we find a transition from an…

This article describes a numerical procedure designed to tune the parameters of periodically-driven dynamical systems to a state in which they exhibit rich dynamical behavior. This is achieved by maximizing the diversity of subharmonic…

Network coherence generally refers to the emergence of simple aggregated dynamical behaviours, despite heterogeneity in the dynamics of the subsystems that constitute the network. In this paper, we develop a general frequency domain…

Certain nonlinear systems can switch between dynamical attractors occupying different regions of phase space, under variation of parameters or initial states. In this work we exploit this feature to obtain reliable logic operations. With…

We report about probabilistic likelihood estimates that are performed on time series using an echo state network with orthogonal recurrent connectivity. The results from tests using synthetic stochastic input time series with temporal…

We consider a generic class of gene circuits affected by nonlinear extrinsic noise. To address this nonlinearity we introduce a general perturbative methodology based on assuming timescale separation between noise and genes dynamics, with…

In this paper, the incremental stability of interconnected switched nonlinear systems is discussed. The nature of switching considered is state-dependent. The incremental stability of the switched interconnected system is a stronger…

This paper studies a power transmission system with both conventional generators (CGs) and distributed energy assets (DEAs) providing frequency control. We consider an operating condition with demand aggregating two dynamic components: one…

Using a stochastic generalization of the Hodgkin–Huxley model, we consider the influence of intrinsic channel noise on the synchronization between the spiking activity of the excitable membrane and an externally applied periodic…

Given a uniformly expanding transitive Markov interval map, we show that within the set of ergodic measures the set of nonadapted ergodic measures is residual in with respect to the topology induced by the $\overline{d}$-metric. This set of…

While Large Language Models and their underlying Transformer architecture are remarkably efficient, they do not reflect how our brain processes and learns a diversity of cognitive tasks such as language, nor how it leverages working memory.…

Local periodic perturbations induce frequency-dependent propagation waves in an excitable spatio-temporally chaotic system. We show how segments of noise-contaminated and chaotic perturbations induce characteristic sequences of excitations…

"Noise-induced volatility" refers to a phenomenon of increased level of fluctuations in the collective dynamics of bistable units in the presence of a rapidly varying external signal, and intermediate noise levels. The archetypical…

We consider the exit problem for a one-dimensional system with random switching near an unstable equilibrium point of the averaged drift. In the infinite switching rate limit, we show that the exit time satisfies a limit theorem with a…

Biological systems rely on robust internal information processing: Survival depends on highly reproducible dynamics of regulatory processes. Biological information processing elements, however, are intrinsically noisy (genetic switches,…

We use the qualitative insight of a planar neuronal phase portrait to detect an excitability switch in arbitrary conductance-based models from a simple mathematical condition. The condition expresses a balance between ion channels that…