Related papers: Multi-Stability in Monotone Input/Output Systems
Networks of globally coupled, noise activated, bistable elements with connection time delays are considered. The dynamics of these systems is studied numerically using a Langevin description and analytically using (1) a Gaussian…
Output feedback stabilization of control systems is a crucial issue in engineering. Most of these systems are not uniformly observable, which proves to be a difficulty to move from state feedback stabilization to dynamic output feedback…
The implementation of a combination of continuous weak measurement and classical feedback provides a powerful tool for controlling the evolution of quantum systems. In this work, we investigate the potential of this approach from three…
For an unknown linear system, starting from noisy open-loop input-state data collected during a finite-length experiment, we directly design a linear feedback controller that guarantees robust invariance of a given polyhedral set of the…
Many-body systems can have multiple equilibria. Though the energy of equilibria might be the same, still systems may resist to switch from an unfavored equilibrium to a favored one. In this paper we investigate occurrence of such phenomenon…
We introduce multi-soliton sets in the two-dimensional medium with the second-harmonic-generating nonlinearity subject to spatial modulation in the form of a triangle of singular peaks. Various families of symmetric and asymmetric sets are…
Positive feedback and cooperativity in the regulation of gene expression are generally considered to be necessary for obtaining bistable expression states. Recently, a novel mechanism of bistability termed emergent bistability has been…
Control theory arose from a need to control synthetic systems. From regulating steam engines to tuning radios to devices capable of autonomous movement, it provided a formal mathematical basis for understanding the role of feedback in the…
A general stability analysis is presented for the determination of the transition from incoherent to coherent behavior in an ensemble of globally coupled, heterogeneous, continuous-time dynamical systems. The formalism allows for the…
This manuscript addresses the analysis and design of feedback laws for the stabilization of bilinear control systems in infinite-dimensional spaces. It first examines weak, strong, and polynomial stabilization within a Hilbert space…
We propose and solve a Hamiltonian model for multidimensional epistastatic interactions between beneficial mutations. The model is able to give rise either to a phase transition between two equilibrium states, without any coexistence, or…
When an interacting many-body system, such as a magnet, is driven in time by an external perturbation, such as a magnetic field,the system cannot respond instantaneously due to relaxational delay. The response of such a system under a…
We here describe the possibility of a synthetic description of the onset of Chaos in many degrees of freedom dynamical systems within the framework of the geometric description of dynamics. We show how this approach to instability helps to…
This article deals with dynamical systems depending on a slowly varying parameter. We present several physical examples illustrating memory effects, such as metastability and hysteresis, which frequently appear in these systems. A…
Self-sustained order can emerge in complex systems due to internal feedback between coupled subsystems. Here, we present our discovery of a non-monotonic emergence of order amidst chaos in a turbulent thermo-acoustic fluid system.…
Mass-action chemical reaction systems are frequently used in Computational Biology. The corresponding polynomial dynamical systems are often large (consisting of tens or even hundreds of ordinary differential equations) and poorly…
Multistability -- the emergence of multiple stable states under identical conditions -- is a hallmark of nonlinear complexity and an enabling mechanism for multilevel optical memory and photonic computing. Its realization in a compact…
Pulse stabilization of cycles with Prediction-Based Control including noise and stochastic stabilization of maps with multiple equilibrium points is analyzed for continuous but, generally, non-smooth maps. Sufficient conditions of global…
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…
The stability of a complex system generally decreases with increasing system size and interconnectivity, a counterintuitive result of widespread importance across the physical, life, and social sciences. Despite recent interest in the…