Boundedness and stability for Cohen–Grossberg neural network with time-varying delays

AbstractIn this paper, a model is considered to describe the dynamics of Cohen–Grossberg neural network with variable coefficients and time-varying delays. Uniformly ultimate boundedness and uniform boundedness are studied for the model by utilizing the Hardy inequality. Combining with the Halanay inequality and the Lyapunov functional method, some new sufficient conditions are derived for the model to be globally exponentially stable. The activation functions are not assumed to be differentiable or strictly increasing. Moreover, no assumption on the symmetry of the connection matrices is necessary. These criteria are important in signal processing and the design of networks

Stability and Bifurcation of a Class of Discrete-Time Cohen-Grossberg Neural Networks with Delays

A class of discrete-time Cohen-Grossberg neural networks with delays is investigated in this paper. By analyzing the corresponding characteristic equations, the asymptotical stability of the null solution and the existence of Neimark-Sacker bifurcations are discussed. By applying the normal form theory and the center manifold theorem, the direction of the Neimark-Sacker bifurcation and the stability of bifurcating periodic solutions are obtained. Numerical simulations are given to illustrate the obtained results

Towards a continuous dynamic model of the Hopfield theory on neuronal interaction and memory storage

The purpose of this work is to study the Hopfield model for neuronal interaction and memory storage, in particular the convergence to the stored patterns. Since the hypothesis of symmetric synapses is not true for the brain, we will study how we can extend it to the case of asymmetric synapses using a probabilistic approach. We then focus on the description of another feature of the memory process and brain: oscillations. Using the Kuramoto model we will be able to describe them completely, gaining the presence of synchronization between neurons. Our aim is therefore to understand how and why neurons can be seen as oscillators and to establish a strong link between this model and the Hopfield approach

Dynamics analysis and applications of neural networks

Ph.DDOCTOR OF PHILOSOPH

International Conference on Mathematical Analysis and Applications in Science and Engineering – Book of Extended Abstracts

The present volume on Mathematical Analysis and Applications in Science and Engineering - Book of Extended Abstracts of the ICMASC’2022 collects the extended abstracts of the talks presented at the International Conference on Mathematical Analysis and Applications in Science and Engineering – ICMA2SC'22 that took place at the beautiful city of Porto, Portugal, in June 27th-June 29th 2022 (3 days). Its aim was to bring together researchers in every discipline of applied mathematics, science, engineering, industry, and technology, to discuss the development of new mathematical models, theories, and applications that contribute to the advancement of scientific knowledge and practice. Authors proposed research in topics including partial and ordinary differential equations, integer and fractional order equations, linear algebra, numerical analysis, operations research, discrete mathematics, optimization, control, probability, computational mathematics, amongst others. The conference was designed to maximize the involvement of all participants and will present the state-of- the-art research and the latest achievements.info:eu-repo/semantics/publishedVersio

Systems evolution: the conceptual framework and a formal model

This research addresses to some of the fundamental problems in systems science.T he aim of this study is to: (1) provide a general conceptual framework for systems evolution; (2) develop a formal model for evolving systems based on dynamical systems theory; (3) analyse the evolving behaviour of various systems by using the formal model so far developed. First of all, it is argued that a system, which can be recognized by an observer as a system, is characterised by some emergent properties at a certain level of discourse. These properties are the results of the interactions between the system as components but not reducible to the individual or summative properties of those components. Any system is such an emergent and organized whole, and this whole can be defined and described as an emergent attractor. To maintain the wholeness in a changing environment, an open system may undergo radical changes both in its structure and function. The process of change is what is called of systems evolution. On reviewing the existing theories of self-organization, such as "Theory of Dissipative Structure", "Synergetics", "Hypercycle", "Cellular Automata", "Random Boolean Network" et al., a general conceptual framework for systems evolution has been outlined and it is based on the concept of emergent attractor for open systems. The emphasis is placed on the structural aspect of the process of change. Modem mathematical dynamical systems theory, with the study of nonlinear dynamics as its core, can provide (a) the concept of "attractor" to describe a system as an organized whole; (b) simple geometrical models of complex behaviour, (c) a complete taxonomy of attractors and bifurcation patterns; (d) a mathematical rationale for the explanations of evolutionary processes. Based on this belief, a formal model of evolving systems has been developed by using the language of mathematical dynamical systems theory (DST). Attractors and emergent attractors are formally defined. It is argued that the state of any systems can be described by one of the four fundamental types of attractors ( i. e. point attractor, periodic attractor, quasiperiodic attractor, chaotic attractor) at a certain level. The evolving behaviour of open systems can be analyzed by looking at the loss of structural stability in the systems. For a full analysis of systems evolution, the emphasis is put on the nonlinear inner dynamics which governs evolving systems. In trying to apply this conceptual framework and formal model, the evolving behaviour of various systems at different levels have been discussed. Among them are Benard cells in hydrodynamics, Brusselator in chemical systems, replicator systems in biology (hypercycle), predator-prey-food systems in ecology, and artificial neural networks. The complex dynamical behaviour of these systems, like the existence of various types of attractors and the occurrences of bifurcation when the environment changes, have been discussed. In most of the examples, the results in previous studies are cited directly and they are only re-interpreted by using the conceptual framework and the formal model developed in this research. In the study of artificial neural networks, a simple cellular automata network with only three neurons has been constructed and the activation dynamics has been analysed according to the formal model. Different attractors representing different dynamical behaviour of this network have been identified (point, periodic, quasiperiodic, and chaotic attractor). Similar discussions have been applied to a coupled Wilson-Cowan net. It is believed that the study of systems evolution is one of those attempts to bring systems science out of its primitive stage in which it ought not to be

Automation and Control Architecture for Hybrid Pipeline Robots

The aim of this research project, towards the automation of the Hybrid Pipeline Robot (HPR), is the development of a control architecture and strategy, based on reconfiguration of the control strategy for speed-controlled pipeline operations and self-recovering action, while performing energy and time management. The HPR is a turbine powered pipeline device where the flow energy is converted to mechanical energy for traction of the crawler vehicle. Thus, the device is flow dependent, compromising the autonomy, and the range of tasks it can perform. The control strategy proposes pipeline operations supervised by a speed control, while optimizing the energy, solved as a multi-objective optimization problem. The states of robot cruising and self recovering, are controlled by solving a neuro-dynamic programming algorithm for energy and time optimization, The robust operation of the robot includes a self-recovering state either after completion of the mission, or as a result of failures leading to the loss of the robot inside the pipeline, and to guaranteeing the HPR autonomy and operations even under adverse pipeline conditions Two of the proposed models, system identification and tracking system, based on Artificial Neural Networks, have been simulated with trial data. Despite the satisfactory results, it is necessary to measure a full set of robot’s parameters for simulating the complete control strategy. To solve the problem, an instrumentation system, consisting on a set of probes and a signal conditioning board, was designed and developed, customized for the HPR’s mechanical and environmental constraints. As a result, the contribution of this research project to the Hybrid Pipeline Robot is to add the capabilities of energy management, for improving the vehicle autonomy, increasing the distances the device can travel inside the pipelines; the speed control for broadening the range of operations; and the self-recovery capability for improving the reliability of the device in pipeline operations, lowering the risk of potential loss of the robot inside the pipeline, causing the degradation of pipeline performance. All that means the pipeline robot can target new market sectors that before were prohibitive