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We track the secondary bifurcations of coherent states in plane Couette flow and show that they undergo an incomplete periodic doubling cascade that ends with a crisis bifurcation. We introduce a symbolic dynamics for the orbits and show…
We study bifurcations of homoclinic orbits to hyperbolic saddle equilibria in a class of four-dimensional systems which may be Hamiltonian or not. Only one parameter is enough to treat these types of bifurcations in Hamiltonian systems but…
Recently, Wang and Xu [ Appl. Math. Lett. 78 (2018) 105-111] studied thresholds and bi-stability in virus-immune dynamics. In this paper, we show there also exist backward bifurcation and saddle node bifurcation in this model. Our…
The Takens-Bogdanov bifurcation is a codimension two bifurcation that provides a key to the presence of complex dynamics in many systems of physical interest. When the system is translation-invariant in one spatial dimension with no…
The bifurcation transition is studied for the onset of intermittency analogous to the Pomeau-Manneville mechanism of type-I, but generalized for the presence of a quasiperiodic external force. The analysis is concentrated on the…
Properties of spatially dependent relaxation oscillations near a SNIPER bifurcation are described. A SNIPER bifurcation creates a large-amplitude long-period periodic orbit via the annihilation of a pair of fixed points in a saddle-node…
An explanation is given for previous numerical results which suggest a certain bifurcation of `vector solitons' from scalar (single-component) solitary waves in coupled nonlinear Schroedinger (NLS) systems. The bifurcation in question is…
Critical phenomena in globally coupled excitable elements are studied by focusing on a saddle-node bifurcation at the collective level. Critical exponents that characterize divergent fluctuations of interspike intervals near the bifurcation…
We find strong evidence for intermittency in forced two dimensional (2D) turbulence in a flowing soap film experiment. In the forward enstrophy cascade the structure function scaling exponents are nearly indistinguishable from 3D studies.…
We consider the system -\Delta u_j + a(x)u_j = \mu_j u_j^3 + \be\sum_{k\ne j}u_k^2u_j, u_j>0, \qquad j=1,...,n, on a possibly unbounded domain $\Om\subset\R^N$, $N\le3$, with Dirichlet boundary conditions. The system appears in nonlinear…
We explore different families of quasi-periodically Forced Logistic Maps for the existence of universality and self-similarity properties. In the bifurcation diagram of the Logistic Map it is well known that there exist parameter values…
In a smooth dynamical system, a homoclinic connection is a closed orbit returning to a saddle equilibrium. Under perturbation, homoclinics are associated with bifurcations of periodic orbits, and with chaos in higher dimensions. Homoclinic…
Three local bifurcations in DC-DC converters are reviewed. They are period-doubling bifurcation, saddle-node bifurcation, and Neimark bifurcation. A general sampled-data model is employed to study the types of loss of stability of the…
By virtue of numerical arguments we study a bifurcation phenomenon occurring for a class of minimization problems associated with the quasi-linear Schrodinger equation.
We analyze, mainly using bifurcation methods, an elliptic superlinear problem in one-dimension with periodic boundary conditions. One of the main novelties is that we follow for the first time a bifurcation approach, relying on a…
Nonlinear normal modes are periodic orbits that survive in nonlinear many-body Hamiltonian systems, and their instability is crucial for relaxation dynamics. Here, we study the instability process of the $\pi/3$-mode in the…
It is well known that quantum tunneling can be described by instantons in the imaginary-time path integral formalism. However, its description in the real-time path integral formalism has been elusive. Here we establish a statement that…
The semi-quantal dynamics is applied to investigate the influence of quantum fluctuations on problems in classical chaos through intermittency involving bifurcations. The results of the numerical calculations indicate that quantum effects…
Many systems can display a very short, rapid changing stage (quasi-discontinuous region) inside a relatively very long and slowly changing process. A quantitative definition for the "quasi-discontinuity" in these systems has been…
Bifurcation problems in which periodic boundary conditions (PBC) or Neumann boundary conditions (NBC) are imposed often involve partial differential equations that have Euclidean symmetry. In this case posing the bifurcation problem with…