Dynamical principles in neuroscience

Dynamical modeling of neural systems and brain functions has a history of success over the last half century. This includes, for example, the explanation and prediction of some features of neural rhythmic behaviors. Many interesting dynamical models of learning and memory based on physiological experiments have been suggested over the last two decades. Dynamical models even of consciousness now exist. Usually these models and results are based on traditional approaches and paradigms of nonlinear dynamics including dynamical chaos. Neural systems are, however, an unusual subject for nonlinear dynamics for several reasons: (i) Even the simplest neural network, with only a few neurons and synaptic connections, has an enormous number of variables and control parameters. These make neural systems adaptive and flexible, and are critical to their biological function. (ii) In contrast to traditional physical systems described by well-known basic principles, first principles governing the dynamics of neural systems are unknown. (iii) Many different neural systems exhibit similar dynamics despite having different architectures and different levels of complexity. (iv) The network architecture and connection strengths are usually not known in detail and therefore the dynamical analysis must, in some sense, be probabilistic. (v) Since nervous systems are able to organize behavior based on sensory inputs, the dynamical modeling of these systems has to explain the transformation of temporal information into combinatorial or combinatorial-temporal codes, and vice versa, for memory and recognition. In this review these problems are discussed in the context of addressing the stimulating questions: What can neuroscience learn from nonlinear dynamics, and what can nonlinear dynamics learn from neuroscience?This work was supported by NSF Grant No. NSF/EIA-0130708, and Grant No. PHY 0414174; NIH Grant No. 1 R01 NS50945 and Grant No. NS40110; MEC BFI2003-07276, and Fundación BBVA

Neural Bursting and Synchronization Emulated by Neural Networks and Circuits

© 2021 IEEE - All rights reserved. This is the accepted manuscript version of an article which has been published in final form at https://doi.org/10.1109/TCSI.2021.3081150Nowadays, research, modeling, simulation and realization of brain-like systems to reproduce brain behaviors have become urgent requirements. In this paper, neural bursting and synchronization are imitated by modeling two neural network models based on the Hopfield neural network (HNN). The first neural network model consists of four neurons, which correspond to realizing neural bursting firings. Theoretical analysis and numerical simulation show that the simple neural network can generate abundant bursting dynamics including multiple periodic bursting firings with different spikes per burst, multiple coexisting bursting firings, as well as multiple chaotic bursting firings with different amplitudes. The second neural network model simulates neural synchronization using a coupling neural network composed of two above small neural networks. The synchronization dynamics of the coupling neural network is theoretically proved based on the Lyapunov stability theory. Extensive simulation results show that the coupling neural network can produce different types of synchronous behaviors dependent on synaptic coupling strength, such as anti-phase bursting synchronization, anti-phase spiking synchronization, and complete bursting synchronization. Finally, two neural network circuits are designed and implemented to show the effectiveness and potential of the constructed neural networks.Peer reviewe

Nonlinear Dynamics, Synchronisation and Chaos in Coupled FHN Cardiac and Neural Cells

Physiological systems are amongst the most challenging systems to investigate from a mathematically based approach. The eld of mathematical biology is a relatively recent one when compared to physics. In this thesis I present an introduction to the physiological aspects needed to gain access to both cardiac and neural systems for a researcher trained in a mathematically based discipline. By using techniques from nonlinear dynamical systems theory I show a number of results that have implications for both neural and cardiac cells. Examining a reduced model of an excitable biological oscillator I show how rich the dynamical behaviour of such systems can be when coupled together. Quantifying the dynamics of coupled cells in terms of synchronisation measures is treated at length. Most notably it is shown that for cells that themselves cannot admit chaotic solutions, communication between cells be it through electrical coupling or synaptic like coupling, can lead to the emergence of chaotic behaviour. I also show that in the presence of emergent chaos one nds great variability in intervals of activity between the constituent cells. This implies that chaos in both cardiac and neural systems can be a direct result of interactions between the constituent cells rather than intrinsic to the cells themselves. Furthermore the ubiquity of chaotic solutions in the coupled systems may be a means of information production and signaling in neural systems

Investigating the role of fast-spiking interneurons in neocortical dynamics

PhD ThesisFast-spiking interneurons are the largest interneuronal population in neocortex. It is well documented that this population is crucial in many functions of the neocortex by subserving all aspects of neural computation, like gain control, and by enabling dynamic phenomena, like the generation of high frequency oscillations. Fast-spiking interneurons, which represent mainly the parvalbumin-expressing, soma-targeting basket cells, are also implicated in pathological dynamics, like the propagation of seizures or the impaired coordination of activity in schizophrenia. In the present thesis, I investigate the role of fast-spiking interneurons in such dynamic phenomena by using computational and experimental techniques. First, I introduce a neural mass model of the neocortical microcircuit featuring divisive inhibition, a gain control mechanism, which is thought to be delivered mainly by the soma-targeting interneurons. Its dynamics were analysed at the onset of chaos and during the phenomena of entrainment and long-range synchronization. It is demonstrated that the mechanism of divisive inhibition reduces the sensitivity of the network to parameter changes and enhances the stability and exibility of oscillations. Next, in vitro electrophysiology was used to investigate the propagation of activity in the network of electrically coupled fast-spiking interneurons. Experimental evidence suggests that these interneurons and their gap junctions are involved in the propagation of seizures. Using multi-electrode array recordings and optogenetics, I investigated the possibility of such propagating activity under the conditions of raised extracellular K+ concentration which applies during seizures. Propagated activity was recorded and the involvement of gap junctions was con rmed by pharmacological manipulations. Finally, the interaction between two oscillations was investigated. Two oscillations with di erent frequencies were induced in cortical slices by directly activating the pyramidal cells using optogenetics. Their interaction suggested the possibility of a coincidence detection mechanism at the circuit level. Pharmacological manipulations were used to explore the role of the inhibitory interneurons during this phenomenon. The results, however, showed that the observed phenomenon was not a result of synaptic activity. Nevertheless, the experiments provided some insights about the excitability of the tissue through scattered light while using optogenetics. This investigation provides new insights into the role of fast-spiking interneurons in the neocortex. In particular, it is suggested that the gain control mechanism is important for the physiological oscillatory dynamics of the network and that the gap junctions between these interneurons can potentially contribute to the inhibitory restraint during a seizure.Wellcome Trust

Discharge Synchrony during the Transition of Behavioral Goal Representations Encoded by Discharge Rates of Prefrontal Neurons

To investigate the temporal relationship between synchrony in the discharge of neuron pairs and modulation of the discharge rate, we recorded the neuronal activity of the lateral prefrontal cortex of monkeys performing a behavioral task that required them to plan an immediate goal of action to attain a final goal. Information about the final goal was retrieved via visual instruction signals, whereas information about the immediate goal was generated internally. The synchrony of neuron pair discharges was analyzed separately from changes in the firing rate of individual neurons during a preparatory period. We focused on neuron pairs that exhibited a representation of the final goal followed by a representation of the immediate goal at a later stage. We found that changes in synchrony and discharge rates appeared to be complementary at different phases of the behavioral task. Synchrony was maximized during a specific phase in the preparatory period corresponding to a transitional stage when the neuronal activity representing the final goal was replaced with that representing the immediate goal. We hypothesize that the transient increase in discharge synchrony is an indication of a process that facilitates dynamic changes in the prefrontal neural circuits in order to undergo profound state changes

Corticonic models of brain mechanisms underlying cognition and intelligence

The concern of this review is brain theory or more specifically, in its first part, a model of the cerebral cortex and the way it:(a) interacts with subcortical regions like the thalamus and the hippocampus to provide higher-level-brain functions that underlie cognition and intelligence, (b) handles and represents dynamical sensory patterns imposed by a constantly changing environment, (c) copes with the enormous number of such patterns encountered in a lifetime bymeans of dynamic memory that offers an immense number of stimulus-specific attractors for input patterns (stimuli) to select from, (d) selects an attractor through a process of “conjugation” of the input pattern with the dynamics of the thalamo–cortical loop, (e) distinguishes between redundant (structured)and non-redundant (random) inputs that are void of information, (f) can do categorical perception when there is access to vast associative memory laid out in the association cortex with the help of the hippocampus, and (g) makes use of “computation” at the edge of chaos and information driven annealing to achieve all this. Other features and implications of the concepts presented for the design of computational algorithms and machines with brain-like intelligence are also discussed. The material and results presented suggest, that a Parametrically Coupled Logistic Map network (PCLMN) is a minimal model of the thalamo–cortical complex and that marrying such a network to a suitable associative memory with re-entry or feedback forms a useful, albeit, abstract model of a cortical module of the brain that could facilitate building a simple artificial brain. In the second part of the review, the results of numerical simulations and drawn conclusions in the first part are linked to the most directly relevant works and views of other workers. What emerges is a picture of brain dynamics on the mesoscopic and macroscopic scales that gives a glimpse of the nature of the long sought after brain code underlying intelligence and other higher level brain functions. Physics of Life Reviews 4 (2007) 223–252 © 2007 Elsevier B.V. All rights reserved

18th IEEE Workshop on Nonlinear Dynamics of Electronic Systems: Proceedings

Proceedings of the 18th IEEE Workshop on Nonlinear Dynamics of Electronic Systems, which took place in Dresden, Germany, 26 – 28 May 2010.:Welcome Address ........................ Page I Table of Contents ........................ Page III Symposium Committees .............. Page IV Special Thanks ............................. Page V Conference program (incl. page numbers of papers) ................... Page VI Conference papers Invited talks ................................ Page 1 Regular Papers ........................... Page 14 Wednesday, May 26th, 2010 ......... Page 15 Thursday, May 27th, 2010 .......... Page 110 Friday, May 28th, 2010 ............... Page 210 Author index ............................... Page XII

Mathematical frameworks for oscillatory network dynamics in neuroscience

The tools of weakly coupled phase oscillator theory have had a profound impact on the neuroscience community, providing insight into a variety of network behaviours ranging from central pattern generation to synchronisation, as well as predicting novel network states such as chimeras. However, there are many instances where this theory is expected to break down, say in the presence of strong coupling, or must be carefully interpreted, as in the presence of stochastic forcing. There are also surprises in the dynamical complexity of the attractors that can robustly appear—for example, heteroclinic network attractors. In this review we present a set of mathemat- ical tools that are suitable for addressing the dynamics of oscillatory neural networks, broadening from a standard phase oscillator perspective to provide a practical frame- work for further successful applications of mathematics to understanding network dynamics in neuroscience