Nonlinear synchrony dynamics of neuronal bursters

We study the appearance of a novel phenomenon for coupled identical bursters: synchronized bursts where there are changes of spike synchrony within each burst. The examples we study are for normal form elliptic bursters where there is a periodic slow passage through a Bautin (codimension two degenerate Andronov-Hopf) bifurcation. This burster has a subcritical Andronov-Hopf bifurcation at the onset of repetitive spiking while the end of burst occurs via a fold limit cycle bifurcation. We study synchronization behavior of two Bautin-type elliptic bursters for a linear direct coupling scheme as well as demonstrating its presence in an approximation of gap-junction and synaptic coupling. We also find similar behaviour in system consisted of three and four Bautin-type elliptic bursters. We note that higher order terms in the normal form that do not affect the behavior of a single burster can be responsible for changes in synchrony pattern; more precisely, we find within-burst synchrony changes associated with a turning point in the spontaneous spiking frequency (frequency transition). We also find multiple synchrony changes in similar system by incorporating multiple frequency transitions. To explain the phenomenon we considered a burst-synchronized constrained model and a bifurcation analysis of the this reduced model shows the existence of the observed within-burst synchrony states. Within-burst synchrony change is also found in the system of mutually delaycoupled two Bautin-type elliptic bursters with a constant delay. The similar phenomenon is shown to exist in the mutually-coupled conductance-based Morris-Lecar neuronal system with an additional slow variable generating elliptic bursting. We also find within-burst synchrony change in linearly coupled FitzHugh-Rinzel 2 3 elliptic bursting system where the synchrony change occurs via a period doubling bifurcation. A bifurcation analysis of a burst-synchronized constrained system identifies the periodic doubling bifurcation in this case. We show emergence of spontaneous burst synchrony cluster in the system of three Hindmarsh-Rose square-wave bursters with nonlinear coupling. The system is found to change between the available cluster states depending on the stimulus. Lyapunov exponents of the burst synchrony states are computed from the corresponding variational system to probe the stability of the states. Numerical simulation also shows existence of burst synchrony cluster in the larger network of such system.Exeter Research Scholarship

Locomotor Network Dynamics Governed By Feedback Control In Crayfish Posture And Walking

Sensorimotor circuits integrate biomechanical feedback with ongoing motor activity to produce behaviors that adapt to unpredictable environments. Reflexes are critical in modulating motor output by facilitating rapid responses. During posture, resistance reflexes generate negative feedback that opposes perturbations to stabilize a body. During walking, assistance reflexes produce positive feedback that facilitates fast transitions between swing and stance of each step cycle. Until recently, sensorimotor networks have been studied using biomechanical feedback based on external perturbations in the presence or absence of intrinsic motor activity. Experiments in which biomechanical feedback driven by intrinsic motor activity is studied in the absence of perturbation have been limited. Thus, it is unclear whether feedback plays a role in facilitating transitions between behavioral states or mediating different features of network activity independent of perturbation. These properties are important to understand because they can elucidate how a circuit coordinates with other neural networks or contributes to adaptable motor output. Computational simulations and mathematical models have been used extensively to characterize interactions of negative and positive feedback with nonlinear oscillators. For example, neuronal action potentials are generated by positive and negative feedback of ionic currents via a membrane potential. While simulations enable manipulation of system parameters that are inaccessible through biological experiments, mathematical models ascertain mechanisms that help to generate biological hypotheses and can be translated across different systems. Here, a three-tiered approach was employed to determine the role of sensory feedback in a crayfish locomotor circuit involved in posture and walking. In vitro experiments using a brain-machine interface illustrated that unperturbed motor output of the circuit was changed by closing the sensory feedback loop. Then, neuromechanical simulations of the in vitro experiments reproduced a similar range of network activity and showed that the balance of sensory feedback determined how the network behaved. Finally, a reduced mathematical model was designed to generate waveforms that emulated simulation results and demonstrated how sensory feedback can control the output of a sensorimotor circuit. Together, these results showed how the strengths of different approaches can complement each other to facilitate an understanding of the mechanisms that mediate sensorimotor integration

A POWER DISTRIBUTION SYSTEM BUILT FOR A VARIETY OF UNATTENDED ELECTRONICS

A power distribution system (PDS) delivers electrical power to a load safely and effectively in a pre-determined format. Here format refers to necessary voltages, current levels and time variation of either as required by the empowered system. This formatting is usually referred as "conditioning". The research reported in this dissertation presents a complete system focusing on low power energy harvesting, conditioning, storage and regulation. Energy harvesting is a process by which ambient energy present in the environment is captured and converted to electrical energy. In recent years, it has become a prominent research area in multiple disciplines. Several energy harvesting schemes have been exploited in the literature, including solar energy, mechanic energy, radio frequency (RF) energy, thermal energy, electromagnetic energy, biochemical energy, radioactive energy and so on. Different from the large scale energy generation, energy harvesting typically operates in milli-watts or even micro-watts power levels. Almost all energy harvesting schemes require stages of power conditioning and intermediate storage - batteries or capacitors that reservoir energy harvested from the environment. Most of the ambient energy fluctuates and is usually weak. The purpose of power conditioning is to adjust the format of the energy to be further used, and intermediate storage smoothes out the impact of the fluctuations on the power delivered to the load. This dissertation reports an end to end power distribution system that integrates different functional blocks including energy harvesting, power conditioning, energy storage, output regulation and system control. We studied and investigated different energy harvesting schemes and the dissertation places emphasis on radio frequency energy harvesting. This approach has proven to be a viable power source for low-power electronics. However, it is still challenging to obtain significant amounts of energy rapidly and efficiently from the ambient. Available RF power is usually very weak, leading to low voltage applied to the electronics. The power delivered to the PDS is hard to utilize or store. This dissertation presents a configuration including a wideband rectenna, a switched capacitor voltage boost converter and a thin film flexible battery cell that can be re-charged at an exceptionally low voltage. We demonstrate that the system is able to harvest energy from a commercially available hand-held communication device at an overall efficiency as high as 7.7 %. Besides the RF energy harvesting block, the whole PDS includes a solar energy harvesting block, a USB recharging block, a customer selection block, two battery arrays, a control block and an output block. The functions of each of the blocks have been tested and verified. The dissertation also studies and investigates several potential applications of this PDS. The applications we exploited include an ultra-low power tunable neural oscillator, wireless sensor networks (WSNs), medical prosthetics and small unmanned aerial vehicles (UAVs). We prove that it is viable to power these potential loads through energy harvesting from multiple sources

Understanding spiking and bursting electrical activity through piece-wise linear systems

In recent years there has been an increased interest in working with piece-wise linear caricatures of nonlinear models. Such models are often preferred over more detailed conductance based models for their small number of parameters and low computational overhead. Moreover, their piece-wise linear (PWL) form, allow the construction of action potential shapes in closed form as well as the calculation of phase response curves (PRC). With the inclusion of PWL adaptive currents they can also support bursting behaviour, though remain amenable to mathematical analysis at both the single neuron and network level. In fact, PWL models caricaturing conductance based models such as that of Morris-Lecar or McKean have also been studied for some time now and are known to be mathematically tractable at the network level. In this work we proceed to analyse PWL neuron models of conductance type. In particular we focus on PWL models of the FitzHugh-Nagumo type and describe in detail the mechanism for a canard explosion. This model is further explored at the network level in the presence of gap junction coupling. The study moves to a different area where excitable cells (pancreatic beta-cells) are used to explain insulin secretion phenomena. Here, Ca2+ signals obtained from pancreatic beta-cells of mice are extracted from image data and analysed using signal processing techniques. Both synchrony and functional connectivity analyses are performed. As regards to PWL bursting models we focus on a variant of the adaptive absolute IF model that can support bursting. We investigate the bursting electrical activity of such models with an emphasis on pancreatic beta-cells

Using MapReduce Streaming for Distributed Life Simulation on the Cloud

Distributed software simulations are indispensable in the study of large-scale life models but often require the use of technically complex lower-level distributed computing frameworks, such as MPI. We propose to overcome the complexity challenge by applying the emerging MapReduce (MR) model to distributed life simulations and by running such simulations on the cloud. Technically, we design optimized MR streaming algorithms for discrete and continuous versions of Conway’s life according to a general MR streaming pattern. We chose life because it is simple enough as a testbed for MR’s applicability to a-life simulations and general enough to make our results applicable to various lattice-based a-life models. We implement and empirically evaluate our algorithms’ performance on Amazon’s Elastic MR cloud. Our experiments demonstrate that a single MR optimization technique called strip partitioning can reduce the execution time of continuous life simulations by 64%. To the best of our knowledge, we are the first to propose and evaluate MR streaming algorithms for lattice-based simulations. Our algorithms can serve as prototypes in the development of novel MR simulation algorithms for large-scale lattice-based a-life models.https://digitalcommons.chapman.edu/scs_books/1014/thumbnail.jp

2018 FSDG Combined Abstracts

https://scholarworks.gvsu.edu/fsdg_abstracts/1000/thumbnail.jp