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Systems with delayed feedback can possess chaotic attractors with extremely high dimension, even if only a few physical degrees of freedom are involved. We propose a state space reconstruction from time series data of a scalar observable,…
Multi-scale structures are prevalent in both natural and artificial systems, as they can handle increasing complexity. Several terms are employed almost interchangeably across various application domains to refer to the multi-scale concept…
Proposed to study the dynamics of physiological systems in which the evolution depends on the state in a previous time, the Mackey-Glass model exhibits a rich variety of behaviors including periodic or chaotic solutions in vast regions of…
We analyze superpositions of ortho- and para-Helium states, considering the possible existence of stationary and metastable states in the system. In particular, the metastable superposition of 1s2s ortho and para states seems to be…
Random non-reciprocal interactions between a large number of conserved densities are shown to enhance the stability of the system towards pattern formation. The enhanced stability is an exact result when the number of species approaches…
Employing a nonlinear left-handed transmission line as a model system, we demonstrate experimentally the multi-stability phenomena predicted theoretically for microstructured left-handed metamaterials with a nonlinear response. We show that…
When a system has more than one stable state, how can the stability of these states be compared? This deceptively simple question has important consequences for ecosystems, because systems with alternative stable states can undergo dramatic…
The theory of backward bifurcations provides a criterion for the existence of positive steady states in epidemiological models with parameters where the basic reproductive ratio is less than one. It is often seen in simulations that this…
In this paper, we investigate the feedback stability of multiple-input multiple-output linear time-invariant systems with combined gain and phase information. To begin with, we explore the stability condition for a class of so-called easily…
Linear stability of synchronized states in networks of delay-coupled oscillators depends on the type of interaction, the network and oscillator properties. For inert oscillator response, found ubiquitously from biology to engineering,…
We study the possibility of taking bosonic systems subject to quadratic Hamiltonians and a noisy thermal environment to non-classical stationary states by feedback loops based on weak measurements and conditioned linear driving. We derive…
We explore the effect of all-optical feedback on the steady state dynamics of optomechanical arrays arising from various topologies. First we consider an array comprised of a pair of independent optomechanical cavities coupled reversibly…
When designing a distributed control system, the system designer has a choice in how to connect the different units through communication channels. In practice, noiseless and noisy channels may coexist. Using the standard toy example of…
We are interested in the feedback stabilization of systems described by Hamilton-Jacobi type equations in $\mathbb{R}^n$. A reformulation leads to a a stabilization problem for a multi-dimensional system of $n$ hyperbolic partial…
We analyze the stability and bifurcation structure of steady states in a mechanochemical model of pattern formation in regenerating tissue spheroids. The model couples morphogen dynamics with tissue mechanics via a positive feedback loop:…
We study the stability properties of a control system composed of a dynamical plant and a feedback controller, the latter generating control signals that can be compromised by a malicious attacker. We consider two classes of feedback…
In this paper we consider BIBO stability of systems described by infinite-dimensional linear state-space representations, filling the so far unattended gap of a formal definition and characterization of BIBO stability in this general case.…
A static non-linear homogeneous feedback for a fixed-time stabilization of a linear time-invariant (LTI) system is designed in such a way that the settling time is assigned exactly to a prescribed constant for all nonzero initial…
In this paper we establish a necessary and sufficient stability condition for a stochastic ring network. Such networks naturally appear in a variety of applications within communication, computer, and road traffic systems. They typically…
Robust stability and stochastic stability have separately seen intense study in control theory for many decades. In this work we establish relations between these properties for discrete-time systems and employ them for robust control…