We articulate the design imperatives for machine learning based digital twins for nonlinear
dynamical systems, which can be used to monitor the “health” of the system and anticipate …

Nonlinear tracking control enabling a dynamical system to track a desired trajectory is
fundamental to robotics, serving a wide range of civil and defense applications. In control …

Transitions from incoherent to coherent dynamical states can be observed in various real-
world networks, ranging from neurons to power-grids. These transitions can be explosive or …

In this topical review, we present a brief overview of the different methods and measures to
detect the occurrence of critical transitions in complex systems. We start by introducing the …

Numerous natural and human-made systems exhibit critical transitions whereby slow
changes in environmental conditions spark abrupt shifts to a qualitatively distinct state …

The advent of machine learning (ML) and Artificial intelligence (AI) has brought about a
significant transformation across multiple industries, as it has facilitated the automation of …

Capacitive membrane and inductive channels enable the approach of neural activities in
some equivalent neural circuits, and involvement of memristive term and magnetic flux can …

In the field of complex dynamics, multistable attractors have been gaining significant
attention due to their unpredictability in occurrence and extreme sensitivity to initial …

The benefits of noise to applications of nonlinear dynamical systems through mechanisms
such as stochastic and coherence resonances have been well documented. Recent years …

Reservoir computing (RC) is a simple and efficient model-free framework for forecasting the
behavior of nonlinear dynamical systems from data. Here, we show that there exist …