Mat́ıas Graña

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In this paper we present a method based on a generalized Hamiltonian formalism to associate to a chaotic system of known dynamics a function of the phase space variables with the characteristics of an energy. Using this formalism we have found energy functions for the Lorenz, Rössler, and Chua families of chaotic oscillators. We have theoretically analyzed(More)
We classify indecomposable racks of order p (p a prime). There are 2p−2p−2 isomorphism classes, among which 2p−3p−1 correspond to quandles. In particular, we prove that an indecomposable quandle of order p is affine. As an ingredient of the classification, we prove that the quandle non-abelian second cohomology set of an indecomposable quandle of prime(More)
We have deduced an energy function for a Hindmarsh-Rose model neuron and we have used it to evaluate the energy consumption of the neuron during its signaling activity. We investigate the balance of energy in the synchronization of two bidirectional linearly coupled neurons at different values of the coupling strength. We show that when two neurons are(More)
We argue that maintaining a synchronized regime between different chaotic systems requires a net flow of energy between the guided system and an external energy source. This energy flow can be spontaneously reduced if the systems are flexible enough as to structurally approach each other through an adequate adaptive change in their parameter values. We(More)
A parameter-adaptive rule that globally synchronizes oscillatory Lorenz chaotic systems with initially different parameter values is reported. In principle, the adaptive rule requires access to the three state variables of the drive system but it has been readapted to work with the exclusive knowledge of only one variable, a potential message carrier. The(More)
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