Introduction. The doubling process is deep and wide throughout the foundations of the small-scale sciences — physics, chemistry and biology– as well as within the human-scale sciences — population systems, government systems, and global systems. We should investigate it all no matter where it leads us.
A study that encompasses these process is called period-doubling bifurcation , however, it has a rather specialized language and mathematics. Notwithstanding, references throughout our study will be to many of the leading scholars within this work.
Emails and Letters . Within all these articles, the authors have references to their source materials that are very helpful. A note of thanks is sent to many of these scholars along with questions.
New resources come online all the time. Scholarpedia  is an example and an article by Dr. Charles Tresser of IBM Watson Research Lab has caught our attention. The studies within nonlinear resonance period doubling  and multiscale modeling  are also believed to hold special keys to unlock the concept of doubling.
 Emails and letters to experts-scholars: We will need help so we are seeking out experts within this field of study.
much more to come…