To get the references to be print as you wish you need to change one function in your used bibliography style file research.bst. Search for function format.title and change it to (I added add.period$ " " * to add the period and a blank):
FUNCTION {format.title}
{ title
duplicate$ empty$ 'skip$
{ "t" change.case$
add.period$ " " *
}
if$
"title" bibinfo.check
}
With the following MWE
\RequirePackage{filecontents}
\begin{filecontents}{\jobname.bib}
@Article{mada2005path,
Title = {Path description of conserved quantities of generalized periodic box-ball systems},
Author = {Mada, Jun and Idzumi, Makoto and Tokihiro, Tetsuji},
Year = {2005},
Number = {2},
Pages = {022701},
Volume = {46},
Journal = {Journal of mathematical physics},
Publisher = {AIP Publishing},
}
@Article{maday1988error,
Title = {Error analysis for spectral approximation of the Korteweg-de Vries equation},
Author = {Maday, Y and Quarteroni, A},
Year = {1988},
Number = {3},
Pages = {499--529},
Volume = {22},
Journal = {RAIRO-Mod{\'e}lisation math{\'e}matique et analyse num{\'e}rique},
}
\end{filecontents}
\documentclass{article}
\usepackage{natbib}
\begin{document}
I try to cite here \cite{mada2005path}.
Cross checking citing here \cite{maday1988error}.
\bibliographystyle{research} % Changed research.bst !!!!!!
\bibliography{\jobname}
\end{document}
you get the wished result:

\bibliography{Lit}with\printbibliography, addingaddbibresource{Lit.bib}in the preamble, and deleting\bibliographystyle{}. Hardly any work at all. – Manuel Weinkauf Feb 22 '17 at 10:37\documentclassand a short text between\begin{document}--\end{document}demonstrating the problem (in your case, producing a citation). Since you use a custom bst-file, you will have to provide this one as well in this case, because noone else has access to it and knows what's in there. – Manuel Weinkauf Feb 22 '17 at 10:40FUNCTION {new.block}in a way that inserts a period, or define a new function that does that, and then insert a call to this function inFUNCTION {article}probably afterformat.title "title". But I am not sure if that works and how exactly. Maybe ask someone who actually knows this language. – Manuel Weinkauf Feb 22 '17 at 15:09