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

Dynamical System Analysis of Interacting Hessence Dark Energy in $f(T)$ Gravity