Special Issue information: 

Dynamical neural systems are invariably infinite-dimensional, and understanding these complex biological systems requires techniques beyond the geometrical methods of Poincare and Lyapunov. Cable properties of single neurons are ubiquitous to all biological neuronal networks, and they define a system of higher-dimensional space. The current trends of importing artificial neural network methodologies to model neuronal networks, in which cable properties are filtered through compartments, foreshadow the differences between finite and infinite-dimensional (higher-order) dynamical systems.

 

Yet their exclusion from theoretical studies precludes our understanding of the roles spatially distributed ionic channels, second-messengers,  and intra and extra-synaptic connectivity patterns play in the dynamics of neuronal network function. This complexity ultimately undermines the dynamic states of all higher-order dynamical systems. In particular, complex or irregular dynamics result from vast degrees of freedom of the dynamical system. What are the techniques for grasping such higher-order dynamical systems? For example, cable equations as dynamical systems on infinite dimensional Grassmannian manifold. The totality of the solutions of the cable equation and its multiscalar generalization form an infinite dimensional Grassmannian manifold.

 

This call for papers specifically aimed at theoretical/computational neuroscientists, physicists, and mathematicians interested in exploring the dynamical states of neurons and neuronal networks in their natural environment by utilizing theories underlying complex dynamics in higher-dimensional space associated with multi-scale neuroscience.

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