Heteroclinic loops leading to hyperchaos

Heteroclinic loops leading to hyperchaos

Homoclinic Loops, Heteroclinic Cycles, and Rank One Dynamics

We prove that genuine nonuniformly hyperbolic dynamics emerge when flows in RN with homoclinic loops or heteroclinic cycles are subjected to certain time-periodic forcing. In particular, we establish the emergence of strange attractors and SRB measures with strong statistical properties (central limit theorem, exponential decay of correlations, et cetera). We identify and study the mechanism re...

Next-to-leading electroweak logarithms at two loops

We review a recent calculation of the two-loop next-to-leading logarithmic electroweak corrections to the form factors for massless chiral fermions coupling to an SU(2)×U(1) singlet gauge boson.

Controlling hyperchaos

For a finite-dimensional dynamical system, whose governing equations may or may not be analytically available, we show how to stabilize an unstable orbit in a neighborhood of a "fully"unstable fixed point (i.e., a fixed point at which all eigenvalues of the Jacobian matrix have modulus greater than unity). Only one of the unstable directions is to be stabilized via time-dependent adjustments of...

Hyperchaos Synchronization Usinggbm

This paper presents synchronization of a new autonomous hyperchaotic system. The generalized backstepping technique is applied to achieve hyperchaos synchronization for the two new hyperchaotic systems. Generalized backstepping method is similarity to backstepping. Backstepping method is used only to strictly feedback systems but generalized backstepping method expands this class. Numerical sim...