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This paper with an analysis of coupled chaotic dynamic systems. Specifically, it deals with chaotic systems which are synchronous and capable of exchanging information back and forth. In this context, the concept of “mutual perturbability” is used. If the change in only one part of the system results in change in another part but not vice versa, this aspect of the organization is termed the “master-slave” type. If the change is mutual, the organization is designated “mutually perturbable”. To begin with the analysis, the systems are coupled in the following manner: a signal from the first of these systems, representing a state variable of the system, is sent to the other system and overrides the corresponding variable. Similarly, a signal from the second system arrives at the first system and overrides another variable. The conditions under which the remainder of the state variables can synchronize with one another are examined, in spite of being chaotic and having different initial conditions. It turns out that in some specific cases, it is possible to perturb either of the two systems by altering the other. Due to this coequal status, the term “mutually perturbable synchronization” (as opposed to the earlier “master-slave”) is used to describe this phenomenon. Not all the multiple coupled systems show this phenomenon. Examples of both possibilities are given.