Regenerative memory in time-delayed neuromorphic photonic resonators

We investigate a photonic regenerative memory based upon a neuromorphic oscillator with a delayed self-feedback (autaptic) connection. We disclose the existence of a unique temporal response characteristic of localized structures enabling an ideal support for bits in an optical buffer memory for storage and reshaping of data information. We link our experimental implementation, based upon a nanoscale nonlinear resonant tunneling diode driving a laser, to the paradigm of neuronal activity, the FitzHugh-Nagumo model with delayed feedback. This proof-of-concept photonic regenerative memory might constitute a building block for a new class of neuron-inspired photonic memories that can handle high bit-rate optical signals

Novel Modes of Synchronization and Extreme Events in Coupled Chemical Oscillators

We experimentally and computationally investigate dynamical behaviors in coupled chemical oscillators. These networks of chemical oscillators are created using catalytic Ru(bpy)32+ loaded cation exchange beads submerged in catalyst-free Belousov-Zhabotinsky (BZ) solutions. Various network structures are created by utilizing the photosensitive nature of the Ru(bpy) 32+ catalyst. The response of the oscillators due to light stimuli can be characterized by constructing a phase response curve (PRC). The PRC quantifies the excitatory and inhibitory responses of BZ oscillators due to applied light perturbations as a function of the oscillators\u27 phase. Different initial concentrations of reactants in the BZ reaction solutions can vary the degree in the excitatory and inhibitory regions of the PRC. We explore synchronization in star networks in both excitatory and inhibitory systems. We describe experiments, simulations, and analytical theory that provides a detailed characterization of novel modes of synchronization in chemical oscillator networks. Synchronization of peripheral oscillators coupled through a hub oscillator is exhibited at coupling strengths leading to novel synchronization of the hub with the peripheral oscillators. The heterogenous peripheral oscillators have different phase velocities that give rise to divergence; however, the perturbation from the hub acts to realign the phases by delaying the faster oscillators more than the slower oscillators. A theoretical analysis provides insights into the mechanism of the synchronization. Computational studies into extreme events are investigated using a modified four-variable Oregonator model, which describes the BZ system. Extreme events are ubiquitous throughout biological, natural, social, and financial systems. Examples of such events are epileptic seizures, earthquakes, riots, and stock market crashes. These events are considered rare excursions from the normal dynamics of a system, which are considered aperiodic in occurrence. The consequences that these events have on the system makes the development of models and experimental methods to study these events important. We will describe the appearance of extreme events in the Oregonator system using instantaneous and time-delayed coupling. We will also discuss a proposed mechanism for the sudden appearance of extreme events in both instantaneous and time-delayed coupling

The Resonate-and-fire Neuron: Time Dependent and Frequency Selective Neurons in Neural Networks

The means through which the nervous system perceives its environment is one of the most fascinating questions in contemporary science. Our endeavors to comprehend the principles of neural science provide an instance of how biological processes may inspire novel methods in mathematical modeling and engineering. The application ofmathematical models towards understanding neural signals and systems represents a vibrant field of research that has spanned over half a century. During this period, multiple approaches to neuronal modeling have been adopted, and each approach is adept at elucidating a specific aspect of nervous system function. Thus while bio-physical models have strived to comprehend the dynamics of actual physical processes occurring within a nerve cell, the phenomenological approach has conceived models that relate the ionic properties of nerve cells to transitions in neural activity. Further-more, the field of neural networks has endeavored to explore how distributed parallel processing systems may become capable of storing memory. Through this project, we strive to explore how some of the insights gained from biophysical neuronal modeling may be incorporated within the field of neural net-works. We specifically study the capabilities of a simple neural model, the Resonate-and-Fire (RAF) neuron, whose derivation is inspired by biophysical neural modeling. While reflecting further biological plausibility, the RAF neuron is also analytically tractable, and thus may be implemented within neural networks. In the following thesis, we provide a brief overview of the different approaches that have been adopted towards comprehending the properties of nerve cells, along with the framework under which our specific neuron model relates to the field of neuronal modeling. Subsequently, we explore some of the time-dependent neurocomputational capabilities of the RAF neuron, and we utilize the model to classify logic gates, and solve the classic XOR problem. Finally we explore how the resonate-and-fire neuron may be implemented within neural networks, and how such a network could be adapted through the temporal backpropagation algorithm

Data based identification and prediction of nonlinear and complex dynamical systems

We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin

Pattern formation in oscillatory systems

Synchronization is a kind of ordinary phenomenon in nature, the study of it includes many mathematical branches. Phase space is one of the most powerful inventions of modern mathematical science. There are two variables, the position and velocity, that can describe the 2-dimensional phase space system. For example, the state of pendulum may be specified by its position and its velocity, so its phase space is 2-dimensional. The state of the system at a given time has a unique corresponding point in the phase space. In order to describe the motion of an oscillator, we can talk about its motion in phase space. Self-sustained oscillators exhibit regular rhythms- they revisit the same points time after time. So the stable oscillation state of a self sustained oscillator can be expressed as some closed curve in phase space, and this closed curve is defined as a limit cycle. There are two topics in this dissertation: Kuramoto model and FitzHugh-Nagumo (FHN) model. Kuramoto\u27s original analysis of his model gives the critical synchronization value for K (K is the coupling constant ). He also gives an estimate for the value of order parameter r when K is close to critical point Kc. However when we give different initial values for the oscillators, the order parameters are different after a long time. The objective of the first topic is to give the distribution of the value of order parameter r under different initial conditions. We divide the oscillators to synchronized part and unsynchronized part, and find that the order parameter satisfies a Gaussian distribution. For the second topic, we start with an introduction for oscillatory clusters in the Belousov-Zhabotinsky reaction. The main idea of this topic is to find the phase property of oscillators in the Oregonator and FHN type models with global inhibitory feedback. Numerical simulations suggest that, in many cases, the cubic system has the same phase value as the piecewise linear system. To simplify this model, we reduce the cubic FHN system to piecewise linear system. In a network of two mutually-coupled neural oscillators, a spike time response curve (STRC) describes the period change of an oscillator given by a perturbation of another oscillator. The STRC is used to predict the phase relations of the two-cell network. We also create a spike time difference map that describes the evolution of the neuron\u27s network based on the STRC

Delay dynamics of neuromorphic optoelectronic nanoscale resonators: Perspectives and applications

With the recent exponential growth of applications using artificial intelligence (AI), the development of efficient and ultrafast brain-like (neuromorphic) systems is crucial for future information and communication technologies. While the implementation of AI systems using computer algorithms of neural networks is emerging rapidly, scientists are just taking the very first steps in the development of the hardware elements of an artificial brain, specifically neuromorphic microchips. In this review article, we present the current state of the art of neuromorphic photonic circuits based on solid-state optoelectronic oscillators formed by nanoscale double barrier quantum well resonant tunneling diodes. We address, both experimentally and theoretically, the key dynamic properties of recently developed artificial solid-state neuron microchips with delayed perturbations and describe their role in the study of neural activity and regenerative memory. This review covers our recent research work on excitable and delay dynamic characteristics of both single and autaptic (delayed) artificial neurons including all-or-none response, spike-based data encoding, storage, signal regeneration and signal healing. Furthermore, the neural responses of these neuromorphic microchips display all the signatures of extended spatio-temporal localized structures (LSs) of light, which are reviewed here in detail. By taking advantage of the dissipative nature of LSs, we demonstrate potential applications in optical data reconfiguration and clock and timing at high-speeds and with short transients. The results reviewed in this article are a key enabler for the development of high-performance optoelectronic devices in future high-speed brain-inspired optical memories and neuromorphic computing. (C) 2017 Author(s).Fundacao para a Ciencia e a Tecnologia (FCT) [UID/Multi/00631/2013]European Structural and Investment Funds (FEEI) through the Competitiveness and Internationalization Operational Program - COMPETE 2020National Funds through FCT [ALG-01-0145-FEDER-016432/POCI-01-0145-FEDER-016432]European Commission under the project iBROW [645369]project COMBINA [TEC2015-65212-C3-3-PAEI/FEDER UE]Ramon y Cajal fellowshipinfo:eu-repo/semantics/publishedVersio