Abstract A reaction–diffusion model, known as the Sel’kov–Schnakenberg is considered. The nonlinear stability of constant steady state studied by using a special Liapunov functional and maximum principle for regular solutions.

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.

We consider a chemostat-type model in which a single species feeds on a limiting nutrient supplied at a constant rate. The model incorporates a general nutrient uptake function and two distributed (infinite) delays. The first delay models the fact that the nutrient is partially recycled after the death of the biomass by bacterial decomposition, and the second delay indicates that the growth of ...

The main purpose of the paper is to give discrete-time counterpart for some strong (robust) stability results concerning periodic linear Hamiltonian systems. In the continuoustime version, these results go back to Liapunov and Žukovskii; their deep generalizations are due to Kreı̆n, Gel’fand, and Jakubovič and obtaining the discrete version is not an easy task since not all results migratemutati...

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.