Related papers: Period Doublings in Coupled Parametrically Forced …
We present analytical and numerical results on integrability and transition to chaotic motion for a generalized Ziegler pendulum, a double pendulum subject to an angular elastic potential and a follower force. Several variants of the…
We study in this paper the behavior of a periodically driven nonlinear mechanical system. Bifurcation diagrams are found which locate regions of quasiperiodic, periodic and chaotic behavior within the parameter space of the system. We also…
We present a phenomenological description of the critical slowing down associated with period-doubling bifurcations in discrete dynamical systems. Starting from a local Taylor expansion around the fixed point and the bifurcation parameter,…
We describe non-equilibrium phase transitions in arrays of dynamical systems with cubic nonlinearity driven by multiplicative Gaussian white noise. Depending on the sign of the spatial coupling we observe transitions to ferromagnetic or…
We study the bifurcations and the chaotic behaviour of a periodically forced double-well Duffing oscillator coupled to a single-well Duffing oscillator. Using the amplitude and the frequency of the driving force as control parameters, we…
Using previous results from boundary conformal field theory and integrability, a phase diagram is derived for the 2 dimensional Ising model at its bulk tri-critical point as a function of boundary magnetic field and boundary spin-coupling…
The bifurcation and chaotic behaviour of unidirectionally coupled deterministic ratchets is studied as a function of the driving force amplitude ($a$) and frequency ($\omega$). A classification of the various types of bifurcations likely to…
Coupled oscillator networks often display transitions between qualitatively different phase-locked solutions -- such as synchrony and rotating wave solutions -- following perturbation or parameter variation. In the limit of weak coupling,…
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…
Discrete time-translation symmetry breaking can be observed in periodically-driven systems oscillating at a fraction of the frequency of the driving force. However, with the exception of the parametric instability in period-doubling,…
We consider the dynamics of a periodic chain of N coupled overdamped particles under the influence of noise. Each particle is subjected to a bistable local potential, to a linear coupling with its nearest neighbours, and to an independent…
We describe a limiting case when nonlinear dynamics of an ac-driven semiconductor superlattice in the miniband transport regime is governed by a periodically forced and damped pendulum. We find analytically the conditions for a transition…
We consider the dynamics of a periodic chain of N coupled overdamped particles under the influence of noise, in the limit of large N. Each particle is subjected to a bistable local potential, to a linear coupling with its nearest…
Parametrically driven oscillators can display period-tripling in response to a drive at thrice the resonance frequency. In contrast to the parametric instability for period doubling, the symmetric fixed-point corresponding to the state of…
We examine the conditions for appearance of symmetry breaking bifurcation in damped and periodically driven pendulum in the case of strong damping. We show that symmetry breaking, unlike other nonlinear phenomena, can exist at high…
We numerically study the collective dynamics of dense particle assemblies driven by non-reciprocal pairwise forces of amplitude $\kappa$. At a critical value $\kappa_{\rm c}$, the system undergoes a dynamical phase transition from an…
Anderson localization physics features three fundamental types of eigenstates: extended, localized, and critical, with the third one exhibiting the exotic properties in-between the former two. Confirming the presence of critical states is…
We unfold the codimension-two simultaneous occurrence of a border-collision bifurcation and a period-doubling bifurcation for a general piecewise-smooth, continuous map. We find that, with sufficient non-degeneracy conditions, a locus of…
We study the dynamics of the Forced Logistic Map in the cylinder. We compute a bifurcation diagram in terms of the dynamics of the attracting set. Different properties of the attracting set are considered, as the Lyapunov exponent and, in…
We perform spectral simulations of dynamo for magnetic Prandtl number of one with Taylor-Green forcing. We observe dynamo transition through a supercritical pitchfork bifurcation. Beyond the transition, the numerical simulations reveal…