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.

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