Related papers: Critical transitions for scalar nonautonomous syst…
Bifurcations in a system of coupled maps are investigated. Using symbolic dynamics it is proven that for coupled shift maps the well known space--time--mixing attractor becomes unstable at a critical coupling strength in favour of a…
Multi-field inflation with a curved scalar geometry has been found to support background trajectories that violate the slow-roll, slow-turn conditions and thus have the potential to evade the swampland constraints. In order to understand…
The analysis of global dynamics, particularly the identification and characterization of attractors and their regions of attraction, is essential for complex nonlinear and hybrid systems. Combinatorial methods based on Conley's index theory…
We suggest a new model for the dynamics of a suspension bridge through a system of nonlinear nonlocal hyperbolic differential equations. The equations are of second and fourth order in space and describe the behavior of the main components…
The ability to reliably predict critical transitions in dynamical systems is a long-standing goal of diverse scientific communities. Previous work focused on early warning signals related to local bifurcations (critical slowing down) and…
The coupled Stuart-Landau equation serves as a fundamental model for exploring synchronization and emergent behavior in complex dynamical systems. However, understanding its dynamics from a comprehensive nonlinear perspective remains…
We construct a family of globally defined dynamical systems for a nonlinear programming problem, such that: (a) the equilibrium points are the unknown (and sought) critical points of the problem, (b) for every initial condition, the…
We consider a minimally coupled scalar field with a monomial potential and a perfect fluid in flat FLRW cosmology. We apply local and global dynamical systems techniques to a new three-dimensional dynamical systems reformulation of the…
We establish the relation between local stability of equilibria and slopes of critical curves for a specific class of difference equations. We then use this result to give global behavior results for nonnegative solutions of the system of…
In this work a new non-minimally coupled model is presented, where a generic function $f(R)$ of the scalar curvature factors the usual Einstein-Hilbert action functional, motivated by relevant results obtained from similar models. Its…
We investigate a model of high-dimensional dynamical variables with all-to-all interactions that are random and non-reciprocal. We characterize its phase diagram and show that the model can exhibit chaotic dynamics. We show that the…
We discuss tipping phenomena (critical transitions) in nonautonomous systems using an example of a bistable ecosystem model with environmental changes represented by time-varying parameters [Scheffer et al., Ecosystems, 11 (2008), pp.…
An account is given of the features, of the kind pertaining to q-statistics, of the dynamics at the one-dimensional critical attractors associated to the three familiar routes to chaos, intermittency, period doubling and quasiperiodicity.…
In this letter we investigate acceleration in the flat cosmological model with a conformally coupled phantom field and we show that acceleration is its generic feature. We reduce the dynamics of the model to a 3-dimensional dynamical system…
Motivated by cosmological models of the early universe we analyse the dynamics of the Einstein equations with a minimally coupled scalar field with monomial potentials $V(\phi)=\frac{(\lambda\phi)^{2n}}{2n}$, $\lambda>0$, $n\in\mathbb{N}$,…
The limiting slow dynamics of slow-fast, piecewise-linear, continuous systems of ODEs occurs on critical manifolds that are piecewise-linear. At points of non-differentiability, such manifolds are not normally hyperbolic and so the…
Several important dynamical systems are in $\mathbb{R}^2$, defined by the pair of differential equations $(x',y')=(f(x,y),g(x,y))$. A question of fundamental importance is how such systems might behave quantum mechanically. In developing…
We prove existence of global attractors for damped hyperbolic equations of the form $$\aligned \eps u_{tt}+\alpha(x) u_t+\beta(x)u- \sum_{ij}(a_{ij}(x) u_{x_j})_{x_i}&=f(x,u),\quad x\in \Omega, t\in[0,\infty[, u(x,t)&=0,\quad x\in \partial…
We theoretically study divergent fluctuations of dynamical events at non-ergodic transitions. We first focus on the finding that a non-ergodic transition can be described as a saddle connection bifurcation of an order parameter for a time…
The critical behavior of infinite families of shift symmetric interacting theories with higher derivative kinetic terms (non unitary) is considered. Single scalar theories with shift symmetry are classified according to their upper critical…