Related papers: Constraining safe and unsafe overshoots in saddle-…
We analyze rate-dependent tipping in a fast/slow system with an equilibrium near the fold of a critical manifiold. We find a Hopf bifurcation as the rate parameter increases in the reduced co-moving system. This implies the growth of a…
A central challenge in physics is to describe non-equilibrium systems driven by randomness, such as a randomly growing interface, or fluids subject to random fluctuations that account e.g. for local stresses and heat fluxes not related to…
In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…
Systems that are not smooth can undergo bifurcations that are forbidden in smooth systems. We review some of the phenomena that can occur for piecewise-smooth, continuous maps and flows when a fixed point or an equilibrium collides with a…
Model-free and data-driven prediction of tipping point transitions in nonlinear dynamical systems is a challenging and outstanding task in complex systems science. We propose a novel, fully data-driven machine learning algorithm based on…
Non-autonomous dynamical systems help us to understand the implications of real systems which are in contact with their environment as it actually occurs in nature. Here, we focus on systems where a parameter changes with time at small but…
Bifurcations of dynamical systems, described by a second order differential equations and by an impact condition are studied. It is shown that the variation of parameters when the number of impacts of a periodic solution increases, leads to…
This paper considers the problem of adaptively overriding unsafe actions of a nominal controller in the presence of high-relative-degree nonovershooting constraints and parametric uncertainties. To prevent the design from being coupled with…
Complex systems exhibiting critical transitions when one of their governing parameters varies are ubiquitous in nature and in engineering applications. Despite a vast literature focusing on this topic, there are few studies dealing with the…
This paper explores transverse coordinates for the purpose of orbitally stabilizing periodic motions of nonlinear, control-affine dynamical systems. It is shown that the dynamics of any (minimal or excessive) set of transverse coordinates,…
This review synthesizes recent advancements in understanding tipping points and cascading transitions within the Earth system, framing them through the lens of nonlinear dynamics and complexity science. It outlines the fundamental concepts…
We consider the scalar delay differential equation $$ \dot{x}(t)=-x(t)+f_{K}(x(t-1)) $$ with a nondecreasing feedback function $f_{K}$ depending on a parameter $K$, and we verify that a saddle-node bifurcation of periodic orbits takes place…
The scaling of the time delay near a "bottleneck" of a generic saddle-node bifurcation is well-known to be given by an inverse square-root law. We extend the analysis to several non-generic cases for smooth vector fields. We proceed to…
A cross-diffusion system modeling the information herding of individuals is analyzed in a bounded domain with no-flux boundary conditions. The variables are the species' density and an influence function which modifies the information state…
Escape from a potential well can occur in different physical systems, such as capsize of ships, resonance transitions in celestial mechanics, and dynamic snap-through of arches and shells, as well as molecular reconfigurations in chemical…
Families of regimes for control systems are studied possessing the so called quasi-controllability property that is similar to the Kalman controllability property. A new approach is proposed to estimate the degree of transients overshooting…
We present an algorithm for robust model predictive control with consideration of uncertainty and safety constraints. Our framework considers a nonlinear dynamical system subject to disturbances from an unknown but bounded uncertainty set.…
Bifurcations can cause dynamical systems with slowly varying parameters to transition to far-away attractors. The terms ``critical transition'' or ``tipping point'' have been used to describe this situation. Critical transitions have been…
Nonlinear dynamical systems subjected to a combination of noise and time-varying forcing can exhibit sudden changes, critical transitions or tipping points where large or rapid dynamic effects arise from changes in a parameter that are…
We discuss the dependence of set-valued dynamical systems on parameters. Under mild assumptions which are often satisfied for random dynamical systems with bounded noise and control systems, we establish the fact that topological…