Sincronismo em um modelo metapopulacional de agregação com acoplamento não linear convexo

The present work is part of the result of the author's doctoral dissertation and aims at presenting a metapopulational aggregation model with a density-independent migration rate that allows the choice of the destination site according to its density. A non-linear coupling is produced here, formed by a convex combination of two matrices, one with a local connection and the other with a global connection. The result obtained here guarantees the asymptotic stability of the synchronized attractor and also that the transverse Lyapunov number of the synchronized attractor is given by the product of the orbital Lyapunov number by a quantifier that depends on the migration rate and the eigenvalues of an originating matrix of the connection matrix. From the numerical simulations of the variation of the transversal Lyapunov number in relation to the parameters migration rate and intrinsic reproduction rate of the function that describes the local dynamics, the regions of possible and impossible synchrony are measured. With the simulations of the synchronized orbit with respect to small perturbations, the values of the intrinsic reproduction rate and the migration rate are determined, for which the most synchronization occurs, and it is also determined that there is no synchronization of chaotic orbits.