  In this work, we have carried on dynamical system analysis of hessence field
coupling with dark matter in $f(T)$ gravity. We have analysed the critical
points due to autonomous system. The resulting autonomous system is non-linear.
So, we have approached via the the theory of non-linear dynamical system.We
have noticed very few papers are devoted to this kind of study.Maximum works in
literature are done treating the dynamical system as done in linear dynamical
analysis, which are unable to predict correct evolution.Our work is totally
different from those kind of works.We have used theory of non-linear dynamical
system theory,developed till date,in our analysis.This approach gives totally
different stable solutions, in contrast what the linear analysis would have
predicted. We have discussed the stability analysis in details due to
exponential potential through computational method in tabular form and analyzed
the evolution of the universe. Some plots are drawn to investigate the
behaviour of the system (this plotting technique is different from usual phase
plot, and devised by us.). Interestingly, the analysis shows the universe may
resemble the `cosmological constant' like evolution (i.e., $\Lambda$CDM model
is a subset of the solution set). Also, all the fixed points of our model are
able to avoid Big rip singularity.
