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In general, the behavior of large and complex aggregates of elementary components can not be understood nor extrapolated from the properties of a few components. The brain is a good example of this type of networked systems where some patterns of behavior are observed independently of the topology and of the number of coupled units. Following this insight, we have studied the dynamics of different aggregates of logistic maps according to a particular {it symbiotic} coupling scheme that imitates the neuronal excitation coupling. All these aggregates show some common dynamical properties, concretely a bistable behavior that is reported here with a certain detail. Thus, the qualitative relationship with neural systems is suggested through a naive model of many of such networked logistic maps whose behavior mimics the waking-sleeping bistability displayed by brain systems. Due to its relevance, some regions of multistability are determined and sketched for all these logistic models.
We consider a Kuramoto model of coupled oscillators that includes quenched random interactions of the type used by van Hemmen in his model of spin glasses. The phase diagram is obtained analytically for the case of zero noise and a Lorentzian distrib
The texture of phase space and bifurcation diagrams of two-dimensional discrete maps describing a lattice of interacting oscillators, confined in on-site potentials with deformable double-well shapes, are examined. The two double-well potentials cons
Reconstructing multiple molecularly defined neurons from individual brains and across multiple brain regions can reveal organizational principles of the nervous system. However, high resolution imaging of the whole brain is a technically challenging
In this paper we have considered the problem of parametric sound generation in an acoustic resonator flled with a fluid, taking explicitely into account the influence of the nonlinearly generated second harmonic. A simple model is presented, and its
Understanding the basic operational logics of the nervous system is essential to advancing neuroscientific research. However, theoretical efforts to tackle this fundamental problem are lacking, despite the abundant empirical data about the brain that