5 Modelling mutational degeneration 23 5.1 Error thresholds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 5.1.1 The prototype model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 5.1.2 Methods of analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 5.1.3 Characterization of error thresholds . . . . . . . . . . . . . . . . . . . . ....

We characterize hyperbolic evolution families on a Banach space X by means of spectral properties of the induced semigroup on the spaces C 0 (IR; X) and L p 1. Exponentially dichotomic and hyperbolic evolution families Given a non{autonomous Cauchy problem _ u(t) = A(t)u(t); u(s) = x s 2 X ; t s 2 IR; (nCP) on a Banach space X with possibly unbounded operators A(t), t 2 IR, on X, the solutions ...

We introduce a model of dynamic visco-elasto-plastic evolution in the linearly elastic regime and prove an existence and uniqueness result. Then we study the limit of (a rescaled version of) the solutions when the data vary slowly. We prove that they converge, up to a subsequence, to a quasistatic evolution in perfect plasticity.

I examine the statistical properties of a NKC model of biological evolution in which species interact and compete to maximize their individual fitness. Species are modeled as adaptive walkers moving on deformable fitness landscapes. The nature of these landscapes is controlled by a small set of free parameters; by tuning them, I investigate the different phases of the model and search in partic...

A logarithm representation of evolution operators is defined. Generators of invertible evolution families are characterized by the logarithm representation. In this article, using the logarithm representation, a concept of evolution operators without satisfying the semigroup property is introduced. In conclusion the existence of alternative infinitesimal generator is clarified.