An Infinite 3-D Quasiperiodic Lattice of Chaotic Attractors

Chunbiao Li^a,b, Julien Clinton Sprott^c

^a Jiangsu Key Laboratory of Meteorological Observation and Information Processing, Nanjing University of Information Science & Technology, Nanjing 210044, China
^b Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Nanjing University of Information Science & Technology, Nanjjing 210044, China
^cDepartment of Physics. University of Wisconsin - Madison, Madison, WI 53706, USA

Received 27 July 2017
Received in revised form 8 December 2017
Accepted 9 December 2017
Available online 19 December 2017
Communicated by C. R. Doering

ABSTRACT

A new dynamical system based on Thomas' system is described with infinitely many strange attractors on a 3-D spatial lattice. The mechanism for this multistability is associated with the disturbed offset boosting of sinusoidal functions with different spatial periods. Therefore, the initial condition for offset boosting can trigger a bifurcation, and consequently infinitely many attractors emerge simultaneously. One parameter of the sinusoidal nonlinearity can increase the frequency of the second order derivative of the variables rather than the first order and therefore increase the Lyapunov exponents accordingly. We show examples where the lattice is periodic and where it is quasiperiodic, the latter of which has an infinite variety of attractor types.