Related papers: Basin stability approach for quantifying responses…

The paper presents an approach to the construction of stabilizing feedback for strongly nonlinear systems. The class of systems of interest includes systems with drift which are affine in control and which cannot be stabilized by continuous…

Many high-dimensional complex systems exhibit an enormously complex landscape of possible asymptotic states. Here, we present a numerical approach geared towards analyzing such systems. It is situated between the classical analysis with…

This paper investigates the conditions for the stability and emergence of patterns in a new three-component reaction-diffusion system. The system describes the coexistence and interaction of water reservoirs, vegetation, and bushfire…

In this paper, a dual estimation methodology is developed for both time-varying parameters and states of a nonlinear stochastic system based on the Particle Filtering (PF) scheme. Our developed methodology is based on a concurrent…

This paper presents two schemes to jointly estimate parameters and states of discrete-time nonlinear systems in the presence of bounded disturbances and noise and where the parameters belong to a known compact set. The schemes are based on…

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…

A new measure to characterize stability of complex dynamical systems against large perturbation is suggested, the stability threshold (ST). It quantifies the magnitude of the weakest perturbation capable to disrupt the system and switch it…

We present a theorem that allows to simplify linear stability analysis of periodic and quasiperiodic nonlinear regimes in N-particle mechanical systems (both conservative and dissipative) with different kinds of discrete symmetry. This…

Non-stationary systems are found throughout the world, from climate patterns under the influence of variation in carbon dioxide concentration, to brain dynamics driven by ascending neuromodulation. Accordingly, there is a need for methods…

This article is devoted to the stabilization of two underactuated planar systems, the well-known straight beam-and-ball system and an original circular beam-and-ball system. The feedback control for each system is designed, using the Jordan…

This paper studies a control method for switching stable coexisting attractors of a class of non-autonomous dynamical systems. The central idea is to introduce a continuous path for the system's trajectory to transition from its original…

The basin entropy is a measure that quantifies, in a system that has two or more attractors, the predictability of a final state, as a function of the initial conditions. While the basin entropy has been demonstrated on a variety of…

Stability of dynamical systems is a central topic with applications in widespread areas such as economy, biology, physics and mechanical engineering. The dynamics of nonlinear systems may completely change due to perturbations forcing the…

In this work we propose an Uncertainty Quantification methodology for sedimentary basins evolution under mechanical and geochemical compaction processes, which we model as a coupled, time-dependent, non-linear, monodimensional (depth-only)…

We discuss the analysis and stability of a family of cross-diffusion boundary value problems with nonlinear diffusion and drift terms. We assume that these systems are close, in a suitable sense, to a set of decoupled and linear problems.…

The parametrisation method for invariant manifolds is a powerful technique for deriving reduced-order models in the context of nonlinear vibrating systems, allowing accurate computations of nonlinear normal modes. Thanks to arbitrary order…

Planar wave trains are traveling wave solutions whose wave profiles are periodic in one spatial direction and constant in the transverse direction. In this paper, we investigate the stability of planar wave trains in reaction-diffusion…

Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…

We consider the adaptive control problem for discrete-time, nonlinear stochastic systems with linearly parameterised uncertainty. Assuming access to a parameterised family of controllers that can stabilise the system in a bounded set within…

For a model nonlinear dynamical system, we show how one may obtain its bifurcation behavior by introducing noise into the dynamics and then studying the resulting Langevin dynamics in the weak-noise limit. A suitable quantity to capture the…