Related papers: Non-smooth saddle-node bifurcations III: strange a…
We study the behaviour at tipping points close to (smoothed) non-smooth fold bifurcations in one-dimensional oscillatory forced systems. The focus is the Stommel-Box, and related climate models, which are piecewise-smooth continuous…
We analyze situations where a saddle-node bifurcation occurs on a fractal basin boundary. Specifically, we are interested in what happens when a system parameter is slowly swept in time through the bifurcation. Such situations are known to…
In this paper, we study heterodimensional cycles of two-parameter families of 3-dimensional diffeomorphisms some element of which contains nondegenerate heterodimensional tangencies of the stable and unstable manifolds of two saddle points…
Strange nonchaotic attractors (SNA) arise in quasiperiodically driven systems in the neighborhood of a saddle node bifurcation whereby a strange attractor is replaced by a periodic (torus) attractor. This transition is accompanied by Type-I…
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 present a dynamical system that naturally exhibits two unstable attractors that are completely enclosed by each others basin volume. This counter-intuitive phenomenon occurs in networks of pulse-coupled oscillators with delayed…
In this paper, a two parameters family $F_{\beta_1,\beta_2}$ of maps of the plane living two different subspaces invariant is studied. We observe that, our model exhibits two chaotic attractors $A_i$, $i=0,1$, lying in these invariant…
Two one-parametric bifurcation problems for scalar nonautonomous ordinary differential equations are analyzed assuming the coercivity of the time-dependent function determining the equation and the concavity of its derivative with respect…
Concave in measure and d-concave in measure nonautonomous scalar ordinary differential equations given by coercive and time-compactible maps have similar properties to equations satisfying considerably more restrictive hypotheses. This…
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 probability distribution of finite-time Lyapunov exponents provides an important characterization of dynamical attractors. We study such distributions for strange nonchaotic attractors (SNAs) created through several different mechanisms…
We prove the holding of chaos in the sense of Li-Yorke for a family of four-dimensional discrete dynamical systems that are naturally associated to ODE systems describing coupled oscillators subject to an external non-conservative force,…
This paper is devoted to the study of nonautonomous multivalued semiflows and their associated pullback attractors. For this kind of dynamical systems we are able to characterize the upper and lower bounds of the attractor as complete…
Strange nonchaotic attractors (SNAs) are observed in quasiperiodically driven time--delay systems. Since the largest Lyapunov exponent is nonpositive, trajectories in two such identical but distinct systems show the property of {\it…
In diverse physical systems stable oscillatory solutions devolve into more complicated dynamical behaviour through border-collision bifurcations. Mathematically these occur when a stable fixed point of a piecewise-smooth map collides with a…
We present a comprehensive mechanism for the emergence of rotational horseshoes and strange attractors in a class of two-parameter families of periodically-perturbed differential equations defining a flow on a three-dimensional manifold.…
We study a homoclinic flip bifurcation of case~\textbf{C}, where a homoclinic orbit to a saddle equilibrium with real eigenvalues changes from being orientable to nonorientable. This bifurcation is of codimension two, and it is the lowest…
We investigate the response of quasiperiodically driven nonlinear systems exhibiting strange non- chaotic attractors (SNAs) to deterministic input signals. We show that if one uses two square waves in aperiodic manner as input to a…
Non-conservative loads of the follower type are usually believed to be the source of dynamic instabilities such as flutter and divergence. It is shown that these instabilities (including Hopf bifurcation, flutter, divergence, and…
In this paper are provided some sufficient conditions for a non autonomous scalar differential equation to have saddle node, transcritical and pitchfork bifurcations using higher order derivatives.