<p>Pattern Formation in Coupled Networks with Inhibition and Gap Junctions</p>

In this dissertation we analyze networks of coupled phase oscillators. We consider systems where long range chemical coupling and short range electrical coupling have opposite effects on the synchronization process. We look at the existence and stability of three patterns of activity: synchrony, clustered state and asynchrony. In Chapter 1, we develop a minimal phase model using experimental results for the olfactory system of Limax. We study the synchronous solution as the strength of synaptic coupling increases. We explain the emergence of traveling waves in the system without a frequency gradient. We construct the normal form for the pitchfork bifurcation and compare our analytical results with numerical simulations. In Chapter 2, we study a mean-field coupled network of phase oscillators for which a stable two-cluster solution exists. The addition of nearest neighbor gap junction coupling destroys the stability of the cluster solution. When the gap junction coupling is strong there is a series of traveling wave solutions depending on the size of the network. We see bistability in the system between clustered state, periodic solutions and traveling waves. The bistability properties also change with the network size. We analyze the system numerically and analytically. In Chapter 3, we turn our attention to a very popular model about network synchronization. We represent the Kuramoto model in its original form and calculate the main results using a different technique. We also look at a modified version and study how this effects synchronization. We consider a collection of oscillators organized in m groups. The addition of gap junctions creates a wave like behavior

Intermediate Stable Phase Locked States In Oscillator Networks

The study of nonlinear oscillations is important in a variety of physical and biological contexts (especially in neuroscience). Synchronization of oscillators has been a problem of interest in recent years. In networks of nearest neighbor coupled oscillators it is possible to obtain synchrony between oscillators, but also a variety of constant phase shifts between 0 and pi. We coin these phase shifts intermediate stable phase-locked states. In neuroscience, both individual neurons and populations of neurons can behave as complex nonlinear oscillators. Intermediate stable phase-locked states are shown to be obtainable between individual oscillators and populations of identical oscillators.These intermediate stable phase-locked states may be useful in the construction of central pattern generators: autonomous neural cicuits responsible for motor behavior. In large chains and two-dimenional arrays of oscillators, intermediate stable phase-locked states provide a mechanism to produce waves and patterns that cannot be obtained in traditional network models. A particular pattern of interest is known as an anti-wave. This pattern corresponds to the collision of two waves from opposite ends of an oscillator chain. This wave may be relevant in the spinal central pattern generators of various fish. Anti-wave solutions in both conductance based neuron models and phase oscillator models are analyzed. It is shown that such solutions arise in phase oscillator models in which the nonlinearity (interaction function) contains both higher order odd and even Fourier modes. These modes are prominent in pairs of synchronous oscillators which lose stability in a supercritical pitchfork bifurcation

Neuronal oscillations, information dynamics, and behaviour: an evolutionary robotics study

Oscillatory neural activity is closely related to cognition and behaviour, with synchronisation mechanisms playing a key role in the integration and functional organization of different cortical areas. Nevertheless, its informational content and relationship with behaviour - and hence cognition - are still to be fully understood. This thesis is concerned with better understanding the role of neuronal oscillations and information dynamics towards the generation of embodied cognitive behaviours and with investigating the efficacy of such systems as practical robot controllers. To this end, we develop a novel model based on the Kuramoto model of coupled phase oscillators and perform three minimally cognitive evolutionary robotics experiments. The analyses focus both on a behavioural level description, investigating the robot’s trajectories, and on a mechanism level description, exploring the variables’ dynamics and the information transfer properties within and between the agent’s body and the environment. The first experiment demonstrates that in an active categorical perception task under normal and inverted vision, networks with a definite, but not too strong, propensity for synchronisation are more able to reconfigure, to organise themselves functionally, and to adapt to different behavioural conditions. The second experiment relates assembly constitution and phase reorganisation dynamics to performance in supervised and unsupervised learning tasks. We demonstrate that assembly dynamics facilitate the evolutionary process, can account for varying degrees of stimuli modulation of the sensorimotor interactions, and can contribute to solving different tasks leaving aside other plasticity mechanisms. The third experiment explores an associative learning task considering a more realistic connectivity pattern between neurons. We demonstrate that networks with travelling waves as a default solution perform poorly compared to networks that are normally synchronised in the absence of stimuli. Overall, this thesis shows that neural synchronisation dynamics, when suitably flexible and reconfigurable, produce an asymmetric flow of information and can generate minimally cognitive embodied behaviours

29th Annual Computational Neuroscience Meeting: CNS*2020

Meeting abstracts This publication was funded by OCNS. The Supplement Editors declare that they have no competing interests. Virtual | 18-22 July 202

Pattern formation in electrically coupled pacemaker cells : a thesis presented in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics at Massey University, Manawatū, New Zealand

Figures are re-used with permission.In this thesis we study electrical activity in smooth muscle cells in the absence of external stimulation. The main goal is to analyse a reaction-diffusion system that models the dynamical behaviour where adjacent cells are coupled through passive electrical coupling. We first analyse the dynamics of an isolated muscle cell for which the model consists of three first-order ordinary differential equations. The cell is either excitable, nonexcitable, or oscillatory depending on the model parameters. To understand this we reduce the model to two equations, nondimensionalise, then perform a detailed numerical bifurcation analysis of the nondimensionalised model. One parameter bifurcation diagrams reveal that even though there is no external stimulus the cell can exhibit two fundamentally distinct types of excitability. By computing two-parameter bifurcation diagrams we are able to explain how the cell transitions between the two types of excitability as parameters are varied. We then study the full reaction-diffusion system first through numerical integration. We show that the system is capable of exhibiting a wide variety of spatiotemporal behaviours such as travelling pulses, travelling fronts, and spatiotemporal chaos. Through a linear stability analysis we are able to show that the spatiotemporal patterns are not due to diffusion-driven instability as is often the case for reaction-diffusion systems. It is as a consequence of the nonlinear dynamics of the reaction terms and coupling effect of diffusion. The precise mechanism is not yet well understood, this will be subject of future work. We then examine travelling wave solutions in detail. In particular we show how they relate to homoclinic and heteroclinic solutions in travelling wave coordinates. Finally we review spectral stability analysis for travelling waves and compute the essential spectrum of travelling waves in our system

Handbook of Marine Model Organisms in Experimental Biology

"The importance of molecular approaches for comparative biology and the rapid development of new molecular tools is unprecedented. The extraordinary molecular progress belies the need for understanding the development and basic biology of whole organisms. Vigorous international efforts to train the next-generation of experimental biologists must combine both levels – next generation molecular approaches and traditional organismal biology. This book provides cutting-edge chapters regarding the growing list of marine model organisms. Access to and practical advice on these model organisms have become aconditio sine qua non for a modern education of advanced undergraduate students, graduate students and postdocs working on marine model systems. Model organisms are not only tools they are also bridges between fields – from behavior, development and physiology to functional genomics. Key Features Offers deep insights into cutting-edge model system science Provides in-depth overviews of all prominent marine model organisms Illustrates challenging experimental approaches to model system research Serves as a reference book also for next-generation functional genomics applications Fills an urgent need for students Related Titles Jarret, R. L. & K. McCluskey, eds. The Biological Resources of Model Organisms (ISBN 978-1-1382-9461-5) Kim, S.-K. Healthcare Using Marine Organisms (ISBN 978-1-1382-9538-4) Mudher, A. & T. Newman, eds. Drosophila: A Toolbox for the Study of Neurodegenerative Disease (ISBN 978-0-4154-1185-1) Green, S. L. The Laboratory Xenopus sp. (ISBN 978-1-4200-9109-0)

Respiratory circulation in the abalone Haliotis iris

An integrated description of the respiratory system of the abalone Haliotis iris is presented. These animals are believed to be inherently primitive and still bear the ancestral gastropod gill arrangement, thus allowing physiological examination of a 'living fossil'. Ventilation, gaseous diffusion, blood transport and the anatomical arrangement of the vascular system are examined under a range of conditions. Resting H. iris consume an average of 0.47 µmol 0₂.g live weight⁻¹ .h⁻¹, 87% of which is taken up across the gills, the remainder diffuses directly into the foot and epipodium. A 300g abalone ventilates its gills at a rate of 28mL.min⁻¹, a rate which, due to low resistance to diffusion (diffusion limitation index = 0.47) and a well matched ventilation/perfusion conductance ratio, is adequate to support the quiescent animal. Increased oxygen demand is accommodated by an increase in cardiac stroke volume, elevating output from 9.1 to 24.4 µL.g⁻¹.min⁻¹. At rest the right gill is the predominant gas exchanger, receiving 95.7% of the branchial blood flow, when cardiac output is elevated the left gill becomes equally perfused, effectively doubling the diffusing surface. Ventilation does not increase, and an increased reliance on assistance from external water currents is seen. Previously undescribed components of the vascular system, notably an extensive sinus of mixed venous and arterial blood surrounding the gut and a large vessel that offers a bypass to the right kidney, provide a low resistance circuit between the heart and gills, bypassing the major organs and muscles. The low resistance circuit allows haemolymph to pass from the aorta to the base of the gills with minimal loss of pressure and no phase shift in the pulse, allowing blood to cross the gills with maximal inertia and instantaneous pressure gradient. Haliotis iris therefore appears to have exploited its limited physiological resources to the maximum in the routine operation of its gas exchange system. It is concluded that further improvement could not occur without substantial remodeling of the body plan, which may account for the abandonment of the system by higher gastropods