Systems which involve coupling between continuous and discrete dynamics are
known as Hybrid Systems. We will consider an abstraction of hybrid systems where there
are discrete switching events in a continuous dynamical system. Such systems are known
as Switched Systems. We will address the primary question of the stability of a switched
system.
Another abstraction of hybrid systems is Scalar Signalling networks. It is unrealistic to
assume that in a large network each cell has to have access to complete knowledge of the
state of cells from which it receives inputs. The inputs may be seen in the form of signals,
for example, in neuronal dynamics, the input might typically be zero or small except only
when the other neuron spikes. We will give some interesting examples to illustrate scalar
signals and how they may stabilize or destabilize a system.