Related papers: Experimental Observation of Hidden Multistability …

The periodic modulation of an oscillator's frequency can lead to so-called parametric oscillations at half the driving frequency, which display bistability between two states whose phases differ by \pi. Such phase-locking bistability is at…

We report the first experimental observation of extreme multistability in a controlled laboratory investigation. Extreme multistability arises when infinitely many attractors coexist for the same set of system parameters. The behavior was…

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…

Distinguishability and, by extension, observability are key properties of dynamical systems. Establishing these properties is challenging, especially when no analytical model is available and they are to be inferred directly from…

Multi-stability is a widely observed phenomenon in real complex networked systems, such as technological infrastructures, ecological systems, gene regulation, transportation and more. When a system functions normally but there exists also a…

We show, theoretically and experimentally, the existence of a multi-stable regime in a nonlinear saturable coupler. In spite of its simplicity, we found that this model shows generic and fundamental properties of extended saturable…

It is by now established that, remarkably, the addition of noise to a nonlinear system may sometimes facilitate, rather than hamper the detection of weak signals. This phenomenon, usually referred to as stochastic resonance, was originally…

The oscillatory response of nonlinear systems exhibits characteristic phenomena such as multistability, discontinuous jumps and hysteresis. These can be utilized in applications leading, e.g., to precise frequency measurement, mixing,…

We study synchronization dynamics in populations of coupled phase oscillators with higher-order interactions and community structure. We find that the combination of these two properties gives rise to a number of states unsupported by…

Processes occurring in real open systems are far from equilibrium state and they can lead to synergetic effects, which are caused by coordinated behavior of system units. Traditional methods of analysis often just establish such behavior,…

The main objective of this paper is to show that two asymptotically stable steady states which belong to an analytic path of asymptotically stable steady states can be gradually transferred one to the other by successive changes of the…

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…

We investigate the classical dynamics of optical nonlinear Kerr couplers, focusing on their potential relevance to quantum computing applications. The system consists of three Kerr-type nonlinear oscillators arranged in two configurations:…

We study how the connectivity within a recurrent neural network determines and is determined by the multistable solutions of network activity. To gain analytic tractability we let neural activation be a non-smooth Heaviside step function.…

Hyperexponential stability is investigated for dynamical systems with the use of both, explicit and implicit, Lyapunov function methods. A nonlinear hyperexponential control is designed for stabilizing linear systems. The tuning procedure…

The ever increasing complexity of real-time control systems results in significant deviations in the timing of sensing and actuation, which may lead to degraded performance or even instability. In this paper we present a method to analyze…

Metastability is a ubiquitous phenomenon in non-equilibrium physics and classical stochastic dynamics.It arises when the system dynamics settles in long-lived states before eventually decaying to true equilibria. Remarkably, it has been…

We demonstrate that a quiet state and large-amplitude self-sustained oscillations can co-exist in a carbon nanotube subject to time-independent drive. A feature of the bistability is that it would be hysteresis-free in the absence of noise…

Layered control is essential for managing complexity in large-scale systems, employing progressively coarser models at higher layers. While significant advances have been made for fully observable systems, the theoretical foundations of…

We investigate a resonantly modulated harmonic mode, dispersively coupled to a nonequilibrium few-level quantum system. We focus on the regime where the relaxation rate of the system greatly exceeds that of the mode, and develop a quantum…