  Key features of biological activity can often be captured by transitions
between a finite number of semi-stable states that correspond to behaviors or
decisions. We present here a broad class of dynamical systems that are ideal
for modeling such activity. The models we propose are chaotic heteroclinic
networks with nontrivial intersections of stable and unstable manifolds. Due to
the sensitive dependence on initial conditions, transitions between states are
seemingly random. Dwell times, exit distributions, and other transition
statistics can be built into the model through geometric design and can be
controlled by tunable parameters. To test our model's ability to simulate
realistic biological phenomena, we turned to one of the most studied organisms,
{\it C. elegans}, well known for its limited behavioral states. We
reconstructed experimental data from two laboratories, demonstrating the
model's ability to quantitatively reproduce dwell times and transition
statistics under a variety of conditions. Stochastic switching between dominant
states in complex dynamical systems has been extensively studied and is often
modeled as Markov chains. As an alternative, we propose here a new paradigm,
namely chaotic heteroclinic networks generated by deterministic rules (without
the necessity for noise). Chaotic heteroclinic networks can be used to model
systems with arbitrary architecture and size without a commensurate increase in
phase dimension. They are highly flexible and able to capture a wide range of
transition characteristics that can be adjusted through control parameters.
