A new sufficient condition for asymptotic stability of ordinary differential equations is proposed. Unlike classical Liapunov theory, the time derivative along solutions of the Liapunov function may have positive and negative values. The classical Liapunov approach may be regarded as an infinitesimal version of the present theorem. Verification in practical problems is harder than in the classi...

| A new suucient condition for asymptotic stability of ordinary diierential equations is proposed. Unlike classical Liapunov theory, the time derivative along solutions of the Liapunov function may have positive and negative values. The classical Liapunov approach may be regarded as an innnitesimal version of the present theorem. Veriication in practical problems is harder than in the classical...

In this paper an upper bound for the number of algebraically independent Poincaré-Liapunov constants in a certain basis for planar polynomial differential systems is given. Finally, it is conjectured that an upper bound for the number of functionally independent Poincaré-Liapunov quantities would be m + 3m− 7 where m is the degree of the polynomial differential system. Moreover, the computation...

We argue that the spectrum of Liapunov exponents for long chains of nonlinear oscillators, at large energy per mode, may be well approximated by the Liapunov exponents of products of independent random matrices. If, in addition, statistical mechanics applies to the system, the elements of these random matrices have a distribution which may be calculated from the potential and the energy alone. ...

We discuss the notion of Liapunov exponent for integrate-and-fire (IF) type dynamical systems. In contrast to smooth flows there is a contribution to the IF Liapunov exponent arising from the discontinuous nature of the firing mechanism. Introducing the notion of an IF mode-locked state we are able to show that linear stability is consistent with the requirement of a negative IF Liapunov expone...

The paper deals with a certain class of nonautonomous ordinary third-order nonlinear differential equations   y L y L y L t f y L 2 1 0 3 , , ,  with quasi-derivatives. A criterion of asymptotic stability in Liapunov sense as well as a criterion of instability in Liapunov sense is derived. The results are illustrated by two examples.

Cauchy problem, 19, 136Condition number, 40, 55, 99, 110Contractibility, 183Counterflow equation, 156Critical delay, 167Delay Liapunov function, 138Delay margin, 170Departure from normality, 56Diagonalizable matrix, 55Diagonally dominant matrix, 36Differential inclusion, 45Dissipativity radius, 33Dual norm, 8, 25Dual pair, 25Eccentricity, ...

It is well known that external stability of nonlinear input systems can be investigated by means of a suitable extension of the Liapunov functions method. We prove that a complete characterization by means of continuous Liapunov functions is actually possible, provided that the de nition of external stability is appropriately strengthened.

In this paper, we construct a Liapunov functional for a system of nonlinear integral equations. From that Liapunov functional we are able to establish the existence of periodic solutions to the system by applying some well-known fixed point theorems for the sum of a nonlinear contraction mapping and compact operator.