The Hybrid Equation (HyEQ) Toolbox is implemented in MATLAB/Simulink for the simulation of hybrid dynamical systems. This toolbox is capable of simulating individual and interconnected hybrid systems with inputs. Examples of systems that can be simulated include a bouncing ball on a moving platform, fireflies synchronizing their flashing, and more. The Simulink implementation includes four basic blocks that define the dynamics of a hybrid system. These include a flow map, flow set, jump map, and jump set. The flows and jumps of the system are computed by the integrator system which is comprised of blocks that compute the continuous dynamics of the hybrid system, trigger jumps, update the state of the system and simulation time at jumps, and stop the simulation. Also includes a “lite simulator” which allows for faster simulation without using Simulink.