By J. A. Bergstra, J. Heering, P. Klint
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N). Then, for t ~ 0 and (i = 1,···, n). 1) is bounded. Ui(t) + tTijVj(t) + Ii) .. Li 3=1 ~ dVj(t) . dUi(t) j=1 Ci dt dt di d9j(Ui(t)) . (dUi(t))2 j=1 dUi(t) dt < 0 for t ~ O. Clearly, E(u) is an energy function. 1) is completely stable. The proof is completed. 1). 1) is complete stable. 1). n = 1; 2). n = 2, and a12 = a21 = 0 or a12 = a21 =1= 0; 3). n = 3, a31a23a12 = a13a21a32, and aij = aji = 0 or aijaji =1= 0, (i =1= jji,j = 1,2,3). 5 can be relaxed by introducing some parameters. 1) is completely stable.
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1) has at least one equilibrium point. Proof' Define a mapping
Algebraic Specification (Acm Press Frontier Series) by J. A. Bergstra, J. Heering, P. Klint