Mode locking in a spatially extended neuron model: active soma and compartmental tree

Understanding the mode-locked response of excitable systems to periodic forcing has important applications in neuroscience. For example it is known that spatially extended place cells in the hippocampus are driven by the theta rhythm to generate a code conveying information about spatial location. Thus it is important to explore the role of neuronal dendrites in generating the response to periodic current injection. In this paper we pursue this using a compartmental model, with linear dynamics for each compartment, coupled to an active soma model that generates action potentials. By working with the piece-wise linear McKean model for the soma we show how the response of the whole neuron model (soma and dendrites) can be written in closed form. We exploit this to construct a stroboscopic map describing the response of the spatially extended model to periodic forcing. A linear stability analysis of this map, together with a careful treatment of the non-differentiability of the soma model, allows us to construct the Arnol'd tongue structure for 1:q states (one action potential for q cycles of forcing). Importantly we show how the presence of quasi-active membrane in the dendrites can influence the shape of tongues. Direct numerical simulations confirm our theory and further indicate that resonant dendritic membrane can enlarge the windows in parameter space for chaotic behavior. These simulations also show that the spatially extended neuron model responds differently to global as opposed to point forcing. In the former case spatio-temporal patterns of activity within an Arnol'd tongue are standing waves, whilst in the latter they are traveling waves.

Theory and language of climate change communication

Climate change communication has become a salient topic in science and society. It has grown to be something like a booming industry alongside more established ‘communication enterprises’, such as health communication, risk communication, and science communication. This article situates the theory of climate change communication within theoretical developments in the field of science communication. It discusses the importance and difficulties inherent in talking about climate change to different types of publics using various types of communication tools and strategies. It engages with the difficult issue of the relationship between climate change communication and behavior change, and it focuses, in particular, on the role of language (metaphors, words, strategies, frames, and narratives) in conveying climate change issues to stakeholders. In the process, it attempts to provide an overview of emerging theories of climate change communication, theories that recently have begun to proliferate quite dramatically. In some cases, we can, therefore only provide signposts to the most relevant research that is being carried out with regard to climate change communication without being able to engage with all its aspects. We end with an assessment of how communication could be improved in light of the theories and practices discussed in this article.