INVESTIGATION OF CERTAIN FUNDAMENTAL TYPES OF COMPLEX EQUILIBRIUM STATES IN A THREE DIMENSIONAL SPACE,
FOREIGN TECHNOLOGY DIV WRIGHT-PATTERSON AFB OHIO
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Certain fundamental types of complex equilibrium states are investigated for a system of three autonomous differential equations with analytic right sides or with right sides having a certain finite number of partial derivatives. The equilibrium state in which the real parts of all roots of the characteristic equation are nonzero is said to be simple if this is not the case, the equilibrium state is said to be complex. All possible toplogical structures of complex equilibrium states of the type considered for the general case are established. A necessary and sufficient condition for coarseness of an equlibrium state in a three-dimensional space is determined and a criterion is given by which it is possible to distinguish between the resulting types of complex equilibrium states in terms of number and types of coarse equilibrium states for nearby systems.