J. C.
Sprott
Department of Physics
University of Wisconsin
Madison, WI 53706, USA
July 29, 2026
A simple autonomous four-dimensional quadratic system in which a two-wing Lorenz-like attractor slowly translates through phase space. The translation is produced by a dynamical offset variable u(t); the resulting chaotic motion of the center creates a visual impression of wing flapping. The system is
dx/dt = y - x with representative parameters δ = 0.05
and μ = 0.001. Color is used to indicate the local
largest Lyapunov exponent, with red positive (expanding) and
blue negative (contracting). The animation shows 50 frames at 5
frames per second and loops continuously, spanning approximately 6
x105 time units. A short paper describing the system
has been published in the International Journal of Bifurcation and
Chaos (2026) 2650234 (DOI:
10.1142/S0218127426502342)