I have analyzed a lambda omega system by a RG method and want to add some concluding words after numerical verification. But I can not found any suitable mode. If any one have an idea about the system then kindly reply me.
I have no idea what "lambda omega systems" are, but if they are systems of the form presented in the end of your post, you can use the numerous published epidemic models as an example (search for "SI models" or "SIS models" - they are often used in modelling the spread HIV infection (which is not curable) or of infections that do not grant immunity after recovery).
As the slightly offensive "internet speech" patterns command to say here, "have you been banned in Google?" In other words, try to search for "SIS model" and you'll get tons of results.
https://www.google.com/search?q=sis+model
http://www.ncbi.nlm.nih.gov/pubmed/?term=SIS+model
Have a look at this
http://www.math.fsu.edu/~bertram/lectures/phase.pdf
http://arxiv.org/pdf/0705.0719.pdf
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