  A central problem in systems biology is to identify parameter values such
that a biological model satisfies some behavioral constraints (\eg, time
series). In this paper we focus on parameter synthesis for hybrid
(continuous/discrete) models, as many biological systems can possess multiple
operational modes with specific continuous dynamics in each mode. These
biological systems are naturally modeled as hybrid automata, most often with
nonlinear continuous dynamics. However, hybrid automata are notoriously hard to
analyze --- even simple reachability for hybrid systems with linear
differential dynamics is an undecidable problem. In this paper we present a
parameter synthesis framework based on $\delta$-complete decision procedures
that sidesteps undecidability. We demonstrate our method on two highly
nonlinear hybrid models of the cardiac cell action potential. The results show
that our parameter synthesis framework is convenient and efficient, and it
enabled us to select a suitable model to study and identify crucial parameter
ranges related to cardiac disorders.
