**Antonio Steiner, Martin J. Gander**

*Le soluzioni delle equazioni preda-predatore***Ilse Walker, A. Marques Filho**

*Tilman's (1994) Models of Competition and Biodiversity: Critical Comments*

(**Abstract.**Comparative analysis between Tilman's models (1994) of competition and biodiversity (based on Levin's logistic equation (1969)) and the classical Lotka-Volterra competition models reveals that the major difference is the omission of the mortality rate in the logistic terms in the Levins-Tilman models. This falsifies the equation*r = b - d*(*r =*intrinsic growth rate,*b =*rate of reproduction/colonization,*d =*death rate) and results in an over-estimation of the logistic growth reduction per individual present in the system. Consequently, population growth is reduced to zero before the carrying capacity of the system is reached. )**Andrea Pellegrinelli**

*Modelli per malattie parassitarie: convergenza delle soluzioni nel caso ermafrodita***Mauro Arrigoni, Claudio Marsan, Fabrizio Pini**

*La struttura iperciclica come fattore di coesistenza stabile e garante della biodiversità*

(**Abstract.**This article resumes some models describing the hypercyclic structure of the interaction between different trophic levels, which were already proposed in [2]. The inner dynamics of the uppermost level is modified in a competitive sense. The hypercyclic structure, which constitutes a hierarchically higher stage, exerts an evolutive control function, by slowing down a possible uncontrolled population growth and by mantaining biodiversity. Stability conditions are given for one model and a weaker stability criterion is proposed for a second one. The latter concerns stability restricted to a finite time interval, which is long enough with respect to some characteristic time of the real biological system considered. )