Whistler waves are electromagnetic waves that propagates in warm plasma; they can be found in the magnetosphere and ionosphere, where they are responsible for the acceleration and precipitation of electrons. Those waves are often generated by the whistler anisotropy instability, which is a plasma instability driven by the temperature anisotropy of electrons. The present study addresses the problem of studying with linear theory and PIC methods the onset and the developing of this instability when cold electrons are also present.