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It is well known that instantons are classical topological solutions existingin the context of quantum field theories that lie behind the standard model ofparticles. To provide a better understanding for the dynamical nature ofspinor-type instanton solutions, conformal invariant pure spinor fermionicmodels that admit particle-like solutions for the derived classical fieldequations are studied in this work under cosine wave forcing. For this purposethe effects of external periodic forcing on two systems having differentdimensions and quantum spinor numbers and have been obtained under the use ofHeisenberg ansatz are investigated by constructing their Poincar\'e sections inphase space. As a result, bifurcations and chaos are observed depending on theexcitation amplitude of the external forcing in both pure spinor fermionicmodels.

Unstable Behaviours of Classical Solutions in Spinor-type Conformal Invariant Fermionic Models