Dynamical Systems

Complex systems are pervasive in many areas of science integrated in our daily lives. Examples include financial markets, highway transportation networks, telecommunication networks, world and country economies, social networks, immunological systems, living organisms, computational systems and electrical and mechanical structures. Complex systems are often composed of a large number of interconnected and interacting entities, exhibiting much richer global scale dynamics than the properties and behavior of individual entities. Complex systems are studied in many areas of natural sciences, social sciences, engineering and mathematical sciences. This special issue therefore intends to contribute towards the dissemination of the multifaceted concepts in accepted use by the scientific community. We hope readers enjoy this pertinent selection of papers which represents relevant examples of the state of the art in present day research. [...

Behavioural robustness and the distributed mechanisms hypothesis

A current challenge in neuroscience and systems biology is to better understand properties that allow organisms to exhibit and sustain appropriate behaviours despite the effects of perturbations (behavioural robustness). There are still significant theoretical difficulties in this endeavour, mainly due to the context-dependent nature of the problem. Biological robustness, in general, is considered in the literature as a property that emerges from the internal structure of organisms, rather than being a dynamical phenomenon involving agent-internal controls, the organism body, and the environment. Our hypothesis is that the capacity for behavioural robustness is rooted in dynamical processes that are distributed between agent ‘brain’, body, and environment, rather than warranted exclusively by organisms’ internal mechanisms. Distribution is operationally defined here based on perturbation analyses. Evolutionary Robotics (ER) techniques are used here to construct four computational models to study behavioural robustness from a systemic perspective. Dynamical systems theory provides the conceptual framework for these investigations. The first model evolves situated agents in a goalseeking scenario in the presence of neural noise perturbations. Results suggest that evolution implicitly selects neural systems that are noise-resistant during coupling behaviour by concentrating search in regions of the fitness landscape that retain functionality for goal approaching. The second model evolves situated, dynamically limited agents exhibiting minimalcognitive behaviour (categorization task). Results indicate a small but significant tendency toward better performance under most types of perturbations by agents showing further cognitivebehavioural dependency on their environments. The third model evolves experience-dependent robust behaviour in embodied, one-legged walking agents. Evidence suggests that robustness is rooted in both internal and external dynamics, but robust motion emerges always from the systemin-coupling. The fourth model implements a historically dependent, mobile-object tracking task under sensorimotor perturbations. Results indicate two different modes of distribution, one in which inner controls necessarily depend on a set of specific environmental factors to exhibit behaviour, then these controls will be more vulnerable to perturbations on that set, and another for which these factors are equally sufficient for behaviours. Vulnerability to perturbations depends on the particular distribution. In contrast to most existing approaches to the study of robustness, this thesis argues that behavioural robustness is better understood in the context of agent-environment dynamical couplings, not in terms of internal mechanisms. Such couplings, however, are not always the full determinants of robustness. Challenges and limitations of our approach are also identified for future studies

Modeling complex cell regulation in the zebrafish circadian clock

The interdisciplinary "systems biology" approach of combining traditional biological investigations with tools from the mathematical and computer sciences has enabled novel insights into many highly complex and dynamic biological systems. The use of models has, for instance, revealed much about the intricate feedback mechanisms and acute importance of gene regulatory networks, and one such network of special note is our internal time keeper, or circadian clock. The circadian clock plays a pivotal role in modulating critical physiological processes, and has also been implicated, either directly or indirectly, in a whole range of pathological states. This research project investigates how the underlying dynamics of the circadian clock in the zebrafish model organism may be captured by a mathematical model, considering in particular the entrainment effect due to external cues such as light. Simulated data is contrasted with experimental results from different light regime experiments to validate the model and guide its refinement. Furthermore, various statistical methods are implemented to process the raw data and support its analysis. Extending the initial deterministic approach to take into account stochastic effects and additive population level effects emerges as a powerful means of representing the circadian signal decay in prolonged darkness, as well as light initiated re-synchronization as a strong component of entrainment. Consequently, it emerges that stochastic effects may be considered an essential feature of the circadian clock in zebrafish. A further cornerstone of the project is the implementation of an integrated simulation environment, including a Sequential Monte Carlo parameter estimation function, which succeeds in predicting a range of previously determined and also novel suitable parameter values. However, considerable difficulties in obtaining parameter values that satisfy the entire range of important target values simultaneously highlights the inherent complexity of accurately simulating the circadian clock

Theoretical Approaches in Non-Linear Dynamical Systems

From Preface: The 15th International Conference „Dynamical Systems - Theory and Applications” (DSTA 2019, 2-5 December, 2019, Lodz, Poland) gathered a numerous group of outstanding scientists and engineers who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without great effort of the staff of the Department of Automation, Biomechanics and Mechatronics of the Lodz University of Technology. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our event was attended by over 180 researchers from 35 countries all over the world, who decided to share the results of their research and experience in different fields related to dynamical systems. This year, the DSTA Conference Proceedings were split into two volumes entitled „Theoretical Approaches in Non-Linear Dynamical Systems” and „Applicable Solutions in Non-Linear Dynamical Systems”. In addition, DSTA 2019 resulted in three volumes of Springer Proceedings in Mathematics and Statistics entitled „Control and Stability of Dynamical Systems”, „Mathematical and Numerical Approaches in Dynamical Systems” and „Dynamical Systems in Mechatronics and Life Sciences”. Also, many outstanding papers will be recommended to special issues of renowned scientific journals.Cover design: Kaźmierczak, MarekTechnical editor: Kaźmierczak, Mare