Related papers: Critical transitions for scalar nonautonomous syst…
The occurrence of tracking or tipping situations for a transition equation $x'=f(t,x,\Gamma(t,x))$ is analyzed under the assumptions on concavity in $x$ either of the maps giving rise to the asymptotic equations $x'=f(t,x,\Gamma_\pm(t,x))$…
A critical transition for a system modelled by a concave quadratic scalar ordinary differential equation occurs when a small variation of the coefficients changes dramatically the dynamics, from the existence of an attractor-repeller pair…
A mathematical modeling process for phenomena with a single state variable that attempts to be realistic must be given by a scalar nonautonomous differential equation $x'=f(t,x)$ that is concave with respect to the state variable $x$ in…
A function with finite asymptotic limits gives rise to a transition equation between a "past system" and a "future system". This question is analyzed in the case of nonautonomous coercive nonlinear scalar ordinary differential equations…
The global bifurcation diagrams for two different one-parametric perturbations ($+\lambda x$ and $+\lambda x^2$) of a dissipative scalar nonautonomous ordinary differential equation $x'=f(t,x)$ are described assuming that 0 is a constant…
This work deals with a parametric linear interpolation between an autonomous FitzHugh-Nagumo model and a nonautonomous skewed-problem with the same fundamental structure. This paradigmatic example allows to construct a family of…
One possible framework to interpret the irreversibility transition observed in periodically driven colloidal suspensions is that of a non-equilibrium phase transition towards an absorbing reversible state at low amplitude of the driving…
The authors consider non-autonomous dynamical behavior of wave-type evolutionary equations with nonlinear damping and critical nonlinearity. These type of waves equations are formulated as non-autonomous dynamical systems (namely,…
The purpose of this paper is to give a characterization of the structure of non-autonomous attractors of the problem $u_t= u_{xx} + \lambda u - \beta(t)u^3$ when the parameter $\lambda > 0$ varies. Also, we answer a question proposed in…
In this letter we will study the cosmological dynamical system of an $f(R)$ gravity in the presence of a canonical scalar field $\phi$ with an exponential potential, by constructing the dynamical system in a way that it is render…
In theoretical ecology, models describing the spatial dispersal and the temporal evolution of species having non-overlapping generations are often based on integrodifference equations. For various such applications the environment has an…
In this work we investigate the asymptotic cosmological dynamics of a modified gravity model based on the $f(R,T^\phi)$ theory, where $R$ denotes the Ricci scalar and $T^\phi$ is the trace of the stress-energy tensor of a scalar field.…
The critical dynamics of Model H with a conserved order parameter coupled to a transverse momentum density which describes the gas-liquid or binary-fluid transitions is investigated within the functional renormalization group approach…
Non-reciprocal systems have been shown to sustain time-dependent patterns, most prominently travelling waves. The transition into these time-dependent states generally breaks time-translational invariance, representing a clear deviation…
In this paper we study canonical scalar field models with a varying second slow-roll parameter, that allow transitions between constant-roll eras. In the models with two constant-roll eras it is possible to avoid fine-tunings in the initial…
This paper is concerned with the dynamics of an infinite-dimensional gradient system under small almost periodic perturbations. Under the assumption that the original autonomous system has a global attractor given as the union of unstable…
In this paper we examine the stability of scalar perturbations in nonsingular models which emerge from an interacting vacuum component. The analysis developed in this paper relies on two phenomenological choices for the energy exchange…
The aim of this paper is to analyze the long-time dynamical behavior of the solution for a degenerate wave equation with time-dependent damping term $\partial_{tt}u + \beta(t)\partial_tu = \mathcal{L}u(x,t) + f(u)$ on a bounded domain…
Critical transitions occur in a variety of dynamical systems. Here, we employ quantifiers of chaos to identify changes in the dynamical structure of complex systems preceding critical transitions. As suitable indicator variables for…
Catastrophic transitions, where a system shifts abruptly between alternate steady states, are a generic feature of many nonlinear systems. Recently these regime shift were suggested as the mechanism underlies many ecological catastrophes,…