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Classic results of the dynamical systems theory are extended and used to study the preservation of synchronization in chaotical dynamical systems. This results show that synchronization can be preserved after changes are made to the linear part of the dynamical system. When the Jacobian matrix of the system is evaluated in the hyperbolic points, the sign structure of the eigenvalues of this matrix...
The standard Carleman linearization states that every analytic n-dimensional nonlinear systems is equivalent to an infinite dimensional linear system. In this paper we truncate this linearization and introduce some modification which reduces the error in the truncation process. We applied this modified Carleman linearization to two van der Pol oscillators with slight different frequencies. Each one...
There are many examples of natural processes in which a substance must travel a trajectory, avoiding obstacles to reach an objective, using a mechanism for orientation and navigation. Such mechanism can be implemented using attraction by autowaves. The linear theory [1],[3],[6] lets to predict the conditions in which a reaction-diffusion system [1]-[12] has a raising oscillating behavior in the initial...
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