The bistable brain: a neuronal model with symbiotic interactions
This work provides a naive model for understanding bistability in neural systems, but it is incremental as it builds on existing logistic map frameworks.
The authors studied aggregates of logistic maps with a symbiotic coupling scheme to model neuronal excitation, finding that these systems exhibit bistable behavior similar to the waking-sleeping patterns observed in brain systems, with specific regions of multistability identified.
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.