Synchronization of Clifford-valued neural networks with leakage, time-varying, and infinite distributed delays on time scales

Neural networks (NNs) with values in multidimensional domains have lately attracted the attention of researchers. Thus, complex-valued neural networks (CVNNs), quaternion-valued neural networks (QVNNs), and their generalization, Clifford-valued neural networks (ClVNNs) have been proposed in the last few years, and different dynamic properties were studied for them. On the other hand, time scale calculus has been proposed in order to jointly study the properties of continuous time and discrete time systems, or any hybrid combination between the two, and was also successfully applied to the domain of NNs. Finally, in real implementations of NNs, time delays occur inevitably. Taking all these facts into account, this paper discusses ClVNNs defined on time scales with leakage, time-varying delays, and infinite distributed delays, a type of delays which have been relatively rarely present in the existing literature. A state feedback control scheme and a generalization of the Halanay inequality for time scales are used in order to obtain sufficient conditions expressed as algebraic inequalities and as linear matrix inequalities (LMIs), using two general Lyapunov-like functions, for the exponential synchronization of the proposed model. Two numerical examples are given in order to illustrate the theoretical results

Avalanches and the edge-of-chaos in neuromorphic nanowire networks

The brain's efficient information processing is enabled by the interplay between its neuro-synaptic elements and complex network structure. This work reports on the neuromorphic dynamics of nanowire networks (NWNs), a brain-inspired system with synapse-like memristive junctions embedded within a recurrent neural network-like structure. Simulation and experiment elucidate how collective memristive switching gives rise to long-range transport pathways, drastically altering the network's global state via a discontinuous phase transition. The spatio-temporal properties of switching dynamics are found to be consistent with avalanches displaying power-law size and life-time distributions, with exponents obeying the crackling noise relationship, thus satisfying criteria for criticality. Furthermore, NWNs adaptively respond to time varying stimuli, exhibiting diverse dynamics tunable from order to chaos. Dynamical states at the edge-of-chaos are found to optimise information processing for increasingly complex learning tasks. Overall, these results reveal a rich repertoire of emergent, collective dynamics in NWNs which may be harnessed in novel, brain-inspired computing approaches

2022 roadmap on neuromorphic computing and engineering

Modern computation based on von Neumann architecture is now a mature cutting-edge science. In the von Neumann architecture, processing and memory units are implemented as separate blocks interchanging data intensively and continuously. This data transfer is responsible for a large part of the power consumption. The next generation computer technology is expected to solve problems at the exascale with 10$^{18}$ calculations each second. Even though these future computers will be incredibly powerful, if they are based on von Neumann type architectures, they will consume between 20 and 30 megawatts of power and will not have intrinsic physically built-in capabilities to learn or deal with complex data as our brain does. These needs can be addressed by neuromorphic computing systems which are inspired by the biological concepts of the human brain. This new generation of computers has the potential to be used for the storage and processing of large amounts of digital information with much lower power consumption than conventional processors. Among their potential future applications, an important niche is moving the control from data centers to edge devices. The aim of this roadmap is to present a snapshot of the present state of neuromorphic technology and provide an opinion on the challenges and opportunities that the future holds in the major areas of neuromorphic technology, namely materials, devices, neuromorphic circuits, neuromorphic algorithms, applications, and ethics. The roadmap is a collection of perspectives where leading researchers in the neuromorphic community provide their own view about the current state and the future challenges for each research area. We hope that this roadmap will be a useful resource by providing a concise yet comprehensive introduction to readers outside this field, for those who are just entering the field, as well as providing future perspectives for those who are well established in the neuromorphic computing community

Three dimensional nanowire networks for reservoir computing.

Over the past few decades, machine learning has become integral to our daily lives. Deep learning has revolutionized industry and scientific research, enabling us to solve complex problems that were previously intractable. Similarly, as computer components have become smaller and more efficient, humanity has gained unprecedented access to affordable hardware. However, the looming fundamental limits on transistor sizes have sparked widescale investigation into alternative means of computation that can circumvent the restrictions imposed by conventional computer architecture. One such method, called reservoir computing, maps sequential data onto a higher dimensional space by using deep neural networks or nonlinear dynamical systems found in nature. Networks of nanowires are currently under consideration for a wide range of electronic and optoelectronic applications, and have recently been pursued as potential devices for reservoir computing. Nanowire devices are usually made by sequential deposition, which inevitably leads to the stacking of wires on top of one another. This thesis builds a fully three dimensional simulation of a nanowire network and demonstrates the effect of stacking on the topology of the resulting networks. Perfectly 2D networks are compared with quasi-3D networks, and both are compared to the corresponding Watts Strogatz networks, which are standard benchmark systems. By investigating quantities such as clustering, path length, modularity, and small-world propensity it is shown that the connectivity of the quasi-3D networks is significantly different to that of the 2D networks. This thesis also explores the effects of stacking on the performance in two reservoir computing tasks: memory capacity and nonlinear transformation. After developing a dynamical model that describes the connections between individual nanowires, a comparison of reservoir computing performance is made between 2D and quasi-3D networks. Most previous simulations use the signals from every wire in the network. In this thesis an electrode configuration is used that is a more physically realistic representation of nanowire networks. The result is that the two different network types have a strikingly similar performance in reservoir computing tasks, which is surprising given their radically different topologies. However, there also exist key differences: for large numbers of wires the upper limit on the performance of the 3D networks is significantly higher than in the 2D networks. In addition, the 3D networks appear to be more resilient to changes in the input parameters, generalizing better to noisy training data. Since previous literature suggests that topology plays an important role in computing performance, these results may have important implications for future applications of nanowire networks

Symmetry in Chaotic Systems and Circuits

Symmetry can play an important role in the field of nonlinear systems and especially in the design of nonlinear circuits that produce chaos. Therefore, this Special Issue, titled “Symmetry in Chaotic Systems and Circuits”, presents the latest scientific advances in nonlinear chaotic systems and circuits that introduce various kinds of symmetries. Applications of chaotic systems and circuits with symmetries, or with a deliberate lack of symmetry, are also presented in this Special Issue. The volume contains 14 published papers from authors around the world. This reflects the high impact of this Special Issue

Nonlinear Systems

Open Mathematics is a challenging notion for theoretical modeling, technical analysis, and numerical simulation in physics and mathematics, as well as in many other fields, as highly correlated nonlinear phenomena, evolving over a large range of time scales and length scales, control the underlying systems and processes in their spatiotemporal evolution. Indeed, available data, be they physical, biological, or financial, and technologically complex systems and stochastic systems, such as mechanical or electronic devices, can be managed from the same conceptual approach, both analytically and through computer simulation, using effective nonlinear dynamics methods. The aim of this Special Issue is to highlight papers that show the dynamics, control, optimization and applications of nonlinear systems. This has recently become an increasingly popular subject, with impressive growth concerning applications in engineering, economics, biology, and medicine, and can be considered a veritable contribution to the literature. Original papers relating to the objective presented above are especially welcome subjects. Potential topics include, but are not limited to: Stability analysis of discrete and continuous dynamical systems; Nonlinear dynamics in biological complex systems; Stability and stabilization of stochastic systems; Mathematical models in statistics and probability; Synchronization of oscillators and chaotic systems; Optimization methods of complex systems; Reliability modeling and system optimization; Computation and control over networked systems

Complex Systems Engineering: Designing Advanced Functions In Dynamical And Mechanical Systems

From computation in neural networks to allostery in proteins, numerous natural and artificial systems are comprised of many interacting parts that give rise to advanced functions. To study such complex systems, a diverse array of interdisciplinary tools have been developed that relate the interactions of existing systems to their functions. However, engineering the interactions to perform designed functions in novel systems remains a significant challenge due to the nonlinearities in the interactions and the vast dimensionality of the design space. Here we develop design principles for complex dynamical and mechanical systems at the lowest level of their microstate interactions. In dynamical neural systems, we use methods from control theory and dynamical systems theory to mathematically map precise patterns of neural connectivity to the control of neural states in human and non-human brains (Chapter 2) and to the learning of computations on internal representations in artificial recurrent neural networks (Chapter 4). In mechanical systems, we use methods from algebraic geometry and dynamical systems to mathematically map precise patterns of mechanical constraints to design shape changes as a minimal model of protein allostery and cooperativity (Chapter 6) and to engineer mechanical metamaterials that possess arbitrarily complex shape changes (Chapter 8). These intuitive maps allow us to navigate previously unexplored design spaces in nonlinear and high-dimensional regimes, enabling us to reverse engineer form from function in novel complex systems that have yet to exist