THE STRUCTURE OF BIFURCATIONS OF CRITICAL POINTS OF A DIFFERENTIAL EQUATION WITH SEVERE NON-LINEARITY .

Document Type : Original Article

Author

DEPARTMENT OF MATHEMATICS - MILITARY TECHNICAL COLLEGE - EGYPT.

Abstract

The critical points of an autonomous differential equation of the second order with severe non-linearity , can have a bifurcation structure in a parameter plane (a,b) , -1Gb <1 , similar to the " box-within-a-box " bifurcation structure . This is shown using a recurrence relation having such a bifurcation structure in (a,b) plane , -1 <b <I .