Embodied robots driven by self-organized environmental feedback

The article discusses the functioning of a concept from a linguosynergetic perspective as a spontaneous equipment of the structure of a homeostatic hierarchical complex organized as an open nonlinear system. The research is aimed to investigate the DEATH concept functioning from a linguosynergetic perspective and develop a model for understanding the synergistic interplay of linguistic and contextual factors in the conceptualization of death. To develop the main research hypothesis, general scientific methods like analysis, synthesis, induction, deduction, abstraction, explanation, and description are used. This system is characterized as an open one because it constantly interacts with the external world and is nonlinear, meaning that it has various options for development at the bifurcation point, but only one is chosen. This continuous process of structuring is known as emergence, which means the concept can adapt to new meanings based on the realities of the world around it. Emergence is a result of the selforganizing mechanism, where the system is reorganized and spontaneously equipped with elements that allow it to move to a new level of operation, while maintaining balance by outputting information from the system’s boundaries. However, the system is also influenced by external factors, which can cause conflict and lead to further reorganization. As a result, the emergence process is ongoing and dynamic, with the structure being both a consequence and a cause of the system`s development. Thus, the principle of self-organization, which is the key concept of synergetics, is founded on the notion of instability. In essence, self-organization refers to the spontaneous emergence of order in a system, which results from the interactions and interrelationships between the system`s components. As such, the concept of self-organization is closely linked to the idea of nonlinearity, which posits that small changes in the system`s components can lead to significant changes in the system`s behavior as a whole. In other words, the behavior of the system as a whole is not simply a sum of the behaviors of its individual components, but is instead an emergent property that arises from the complex interactions between those components. The formation of a new system is not merely a sum of its individual parts. This is, due to the way in which the components of the system connect with one another, a phenomenon known as coherence. Coherence acts as a means to coordinate the various components of the system so that they work together in harmony, rather than independently. Additionally, the system`s components change at different rates and are of varying quality. This process is responsible for the system`s evolutionary nature and reinforces the principle of evolutionary holism in synergetics. This principle is concerned with understanding the mechanisms by which the system`s components come together to form a whole. In summary, the concept is formed in the human mind through a collection of thoughts, which can take on various forms such as lexical and semantic fields, modes, frames, and emotions. The specific form the concept takes depends on the level at which the bifurcation point impacts the fluctuation of the conceptual structure and discursive environment. Essentially, the concept arises from a system that is in an unstable state and is subject to fluctuations that threaten its structure. When the system reaches the bifurcation point, the individual selects one of the possible models for the concept`s development, and this results in a transition from “chaos” to “order” as the concept gains verbal representation. The activation of a concept in one`s cognition occurs at different intensities and is dependent on several factors. These factors include the individual’s level of knowledge about the concept, their principles and beliefs, their interests, their life experiences, as well as extralinguistic factors. The activation of a concept can occur in varying degrees, with some individuals having a more profound understanding of a concept compared to others. Additionally, the process of concept activation can be influenced by external factors such as societal norms and cultural beliefs. Therefore, the way in which a person perceives and activates a concept is a complex and individualized process, influenced by both internal and external factors.

Ann-Shyn Chiang

Swarm intelligence, inspired by the collective behavior observed in social organisms, has emerged as a powerful paradigm in both natural and artificial systems. The concept of a swarm refers to a large group of simple agents that interact locally with one another and their environment, giving rise to complex and intelligent behavior at the group level. Swarm intelligence, on the other hand, represents the ability of a swarm to self-organize, adapt, and solve complex problems without central control. In nature, swarms of social insects such as bees, ants, termites, and birds exhibit remarkable abilities in foraging, navigation, resource allocation, and defense. These organisms demonstrate how the interactions of simple individuals can lead to efficient and robust solutions to various challenges faced in their environments. In artificial systems, researchers have successfully translated the principles of swarm intelligence into algorithms and techniques for optimization, decision-making, and problem-solving. Popular swarm intelligence algorithms, such as Ant Colony Optimization, Particle Swarm Optimization, and Artificial Bee Colony, have shown great promise in tackling complex optimization and search tasks. This paper provides an overview of the fundamental concepts of swarm intelligence and explores the similarities and differences between natural and artificial swarms. It delves into the principles of self-organization, decentralized decision-making, and adaptation that underpin swarm intelligence, allowing these systems to cope with dynamic and uncertain environments. Furthermore, the paper examines the application domains of swarm intelligence, ranging from robotics and autonomous systems to data clustering, image processing, and network routing. The potential of swarm robotics in solving real-world challenges, such as environmental monitoring, disaster response, and precision agriculture, is also explored. Swarm intelligence presents a compelling avenue for understanding and harnessing emergent collective behavior in both biological and computational contexts. The interplay of simplicity, local interactions, and adaptation enables swarms to tackle complex problems efficiently, making them a valuable source of inspiration for the design of intelligent systems in various fields. The study of swarm intelligence continues to advance, offering exciting possibilities for creating adaptive, robust, and scalable solutions in the ever-evolving landscape of artificial intelligence and beyond.

Bifurcation theory is a subject with classical mathematical origin. The modern development of this subject dates back to the pioneering work of Poincare, and over the past four decades this theory has witnessed rapid developments with new ideas and methods from dynamical systems theory, singularity theory and many others. This subject relates to the mathematical study of possible changes in the qualitative or topological structure of parameter-dependent systems (families). Bifurcations occur in both continuous systems (described by ODEs, DDEs or PDEs), and discrete systems (described by maps). It is useful to place the subject of bifurcations in two principal classes such as local and global. Local bifurcations occur when variations in parameters cause changes in the stability of equilibrium (or fixed point). The topological changes in the phase portrait of the system may be confined to arbitrarily small neighborhoods of the bifurcating fixed points by moving the bifurcation parameter close to the bifurcation point (hence ‘local’). It is worth to recall that local bifurcations can produce changes in global behavior and that in the mathematical analysis of local bifurcations problems it is necessary to understand global dynamics, i.e., “punctual singularities can be a concentration of global information”. Global bifurcations occur when ‘larger’ invariant sets such as periodic orbits collide with equilibria. This brings changes in the topology of the trajectories in the phase space which cannot be confined to

The FitzHugh–Nagumo model is improved to consider the effect of the electromagnetic induction on single neuron. On the basis of investigating the Hopf bifurcation behavior of the improved model, stochastic resonance in the stochastic version is captured near the bifurcation point. It is revealed that a weak harmonic oscillation in the electromagnetic disturbance can be amplified through stochastic resonance, and it is the cooperative effect of random transition between the resting state and the large amplitude oscillating state that results in the resonant phenomenon. Using the noise dependence of the mean of interburst intervals, we essentially suggest a biologically feasible clue for detecting weak signal by means of neuron model with subcritical Hopf bifurcation. These observations should be helpful in understanding the influence of the magnetic field to neural electrical activity.

We review recent work concerning the effects of dendritic structure on single neuron response and the dynamics of neural populations. We highlight a number of concepts and techniques from physics useful in studying the behaviour of the spatially extended neuron. First we show how the single neuron Green's function, which incorporates details concerning the geometry of the dendritic tree, can be determined using the theory of random walks. We then exploit the formal analogy between a neuron with dendritic structure and the tight-binding model of excitations on a disordered lattice to analyse various Dyson-like equations arising from the modelling of synaptic inputs and random synaptic background activity. Finally, we formulate the dynamics of interacting populations of spatially extended neurons in terms of a set of Volterra integro-differential equations whose kernels are the single neuron Green's functions. Linear stability analysis and bifurcation theory are then used to investigate two particular aspects of population dynamics (i) pattern formation in a strongly coupled network of analog neurons and (ii) phase-synchronization in a weakly coupled network of integrate-and-fire neurons.

Under study is the mathematical model describing the inverse temperature hysteresis as well as the self-sustained oscillations in the CO oxidation over a palladium catalyst in an chemical stirred tank reactor (CSTR). We consider the reaction dynamics under temperature-programmed conditions: At first, the temperature T of the CSTR monotonically increases (due to outside heating) and then it decreases to the initial value. As the temperature goes up, on the surface and in the bulk of the catalyst two palladium oxide forms appear and then, while the temperature decreases, the catalyst reduces to its original state. The mathematical model of nonstatinary processes in such a CSTR is the piecewise continuous system of nonlinear ordinary differential equations (ODE), i.e, a discrete-continuous system. Using the theory of dynamical systems and bifurcation theory as well as numerical methods, we study the structure of the maximal families of the steady states and periodic solutions in dependence on temperature. For the system under study some sufficient conditions are given under which an inverse hysteresis is observed on the dependence of the conversion of the main reagent versus T. Moreover, as temperature decreases, there are self-oscillations of the reaction rate and CO conversion on the lower back branch of the hysteresis. The parameters of the model are found such that the experimental data are qualitatively described.

The understanding of atmospheric and oceanic low-frequency variability is an old problem having both theoretical interest and practical importance, e.g., for the assessment of climate change. In this paper possible relations with dynamical systems theory are given, in particular through bifurcation theory. Firstly, a specific type of oceanic low frequency variability is described, the so-called Atlantic Multidecadal Oscillation (AMO). Then recent work is reviewed, that investigates bifurcations as these occur in a few low-order models of the atmospheric circulation. It is shown that the Shil′nikov bifurcation in the Hopf-saddle-node bifurcation scenario takes place in each of the above atmospheric models. Related strange attractors and intermittency behavior are also found, both in agreement with the theoretical expectations and with qualitative aspects of the climate variability, like the AMO. It is discussed how the latter connection may be consolidated in higher dimensional and in PDE models.

The relevance of this article was determined by the significance of objectively understanding nonlinear, chaotic systems, which are a product of the dynamic nature of modern science and are addressed by synergetics. The study aimed to conduct a theoretical investigation into the objectivity of scientific knowledge by employing synergetics as a non-traditional scientific paradigm within the contemporary philosophy of science and other interdisciplinary domains. The research methods applied included theoretical, historical, and interdisciplinary approaches, as well as mathematical modelling. It has been established that synergetics represents a meta-approach that emerged both as a response to the crises of the 20th and 21st centuries and as a consequence of globalisation, technological progress, and a shift in the perception of natural processes. It has been determined that synergetics, as a scientific discipline, and the synergetic approach, as an interdisciplinary method of scientific inquiry, enable an objective examination of non-equilibrium and nonlinear transformational processes due to the presence of a theoretical and mathematical framework. It has been generalised that the objectivity of scientific knowledge in synergetics is ensured by methods such as nonlinear thermodynamics of non-equilibrium processes, nonlinear oscillation theory in radio-technical systems, differential typology, catastrophe theory, tensor analysis, non-equilibrium statistical physics, qualitative theory of differential equations, and dynamical systems theory. It has been noted that the methodological and statistical framework of synergetics, as a universal method complementing cybernetics, is a composite approach incorporating elements from various fields of scientific inquiry. The study has demonstrated that within the synergetic paradigm, the concept of “chaos” has been reinterpreted, shifting from a destructive force to a creative source of alternative order through the process of self-organisation, which generates order from chaos. It has been indicated that synergetics represents a paradigm for the emergence of new qualities and provides a mathematical explanation of their development by applying nonlinear differential equations and bifurcation theory, which characterise the transition from quantitative changes to qualitatively new states. The practical significance of this study lies in presenting a new perspective on the objectivity of scientific knowledge, grounded in an understanding of the dynamics of self-organisation in complex systems, thereby facilitating the development of comprehensive approaches to addressing contemporary challenges within interdisciplinary frameworks

In this paper, the tools of dynamical systems theory are applied to examine the streamline patterns and their local and global bifurcations for ciliary-induced peristalsis of non-Newtonian fluid (blood) with the suspension of hybrid nanoparticles (Cu-Ag/Phan-Thien-Tanner based fluid) in a tube with heat source effect. The thermodynamics of this model are recently described by Ali et al. (Biomech Model Mechanobiol 20:2393-2412, 2021), where the fluid flows through a tube whose inner walls are considered to be ciliated with small hair-like structures. However, our novel approach allows us to create a complete picture of the model's overall dynamic behavior in terms of bifurcation point analysis exhibiting qualitatively different flow modes. Special attention is paid to the computing, analysis and simulation of equilibrium points in terms of capturing the global dynamics, such as evaluating the heteroclinic bifurcation, which is used to identify trapping phenomena in response to biological characteristics such as wave amplitude, Weissenberg and wave numbers. The main novelty here is the ability to control the position of the equilibrium points in the domain of interest, allowing one to identify global bifurcations that reflect key dynamic properties of the model. Based on the advantages of this technique, the maximum trapping volume and symmetric trapping zones adjacent to the walls are determined as a novel result. We also show that as the solid volume fraction of copper and the Brinkman number increases, the isotherm patterns become more distorted. Our findings highlight a novel class of complex behavior that governs transitions between qualitatively different modes and trapping phenomena.

Neurons in the brain have rich and adaptive input-output properties. Features such as heterogeneous f-I curves and spike frequency adaptation are known to place single neurons in optimal coding regimes when facing changing stimuli. Yet, it is still unclear how brain circuits exploit single-neuron flexibility, and how network-level requirements may have shaped such cellular function. To answer this question, a multi-scaled approach is needed where the computations of single neurons and neural circuits must be considered as a complete system. In this work, we use artificial neural networks to systematically investigate single-neuron input-output adaptive mechanisms, optimized in an end-to-end fashion. Throughout the optimization process, each neuron has the liberty to modify its nonlinear activation function parametrized to mimic f-I curves of biological neurons, either by learning an individual static function or via a learned and shared adaptation mechanism to modify activation functions in real-time during a task. We find that such adaptive networks show much-improved robustness to noise and changes in input statistics. Using tools from dynamical systems theory, we analyze the role of these emergent single-neuron properties and argue that neural diversity and adaptation play an active regularization role, enabling neural circuits to optimally propagate information across time. Finally, we outline similarities between these optimized solutions and known coding strategies found in biological neurons, such as gain scaling and fractional order differentiation/integration.

We explore a planar discrete-time model from population dynamics subject to a general aperiodic time-varying environment in order to illustrate the recent theory of nonautonomous dynamical systems. Given such a setting, the mathematical standard tools from classical dynamical systems and bifurcation theory cannot be employed, since, for instance, equilibria typically do not exist or eigenvalues yield no stability information. For this reason, we apply a combination of contemporary analytical and numerical techniques adequate to tackle such situations.

This paper details the non-linear dynamic behaviours and control of a non-linear semi-active suspension system using a quarter-car model under kinematic excitation by a road surface profile. The results of local and global bifurcation analysis indicate that the hysteretic non-linear characteristics of damping force cause the suspension system to exhibit codimension-two bifurcation, resulting in homoclinic orbits and a pitchfork bifurcation. The complex dynamic behaviour of automotive suspension systems was examined using a bifurcation diagram, phase portraits, a Poincaré map, and frequency spectra. We also used Lyapunov exponent to identify the occurrence of chaotic motion and verify our analysis. Finally, a dither signal control was used to convert chaotic behaviours into periodic motion. Simulation results verify the effectiveness of the proposed control method.

Aim. The aim of the work is to study the history of ideas about coarseness (structural stability), which is not only one of the most important concepts of the theory of nonlinear systems, but lies at the heart of our worldview. To nowаdays, structural stability has been considered in historical terms only fragmentarily (mainly in connection with the Andronov school) and has not been the subject of a consistent historical study. Method. The study is based on an analysis of original works, historical and scientific literature with the involvement of the memories of participants in the events described. Results. In Andronov’s school, in the context of applied problems, two-dimensional systems for which structural stability is a typical property have been exhaustively studied. Since the late 1950s there is a shift in research on structural stability in the context of applied problems towards the theory of dynamical systems. M. Peixoto studied structural stability on closed two-dimensional manifolds and proved the density of such systems. S. Smale hypothesized the existence of structurally stable systems in the multidimensional case (𝑛 > 3) . Such systems exist (Morse-Smale systems), but he himself established their atypicality, they do not constitute a dense set. Multidimensional systems are characterized by complex behavior; an example of such a system (Smale’s horseshoe) was built. The study of systems with complex behavior stimulated the development of hyperbolic theory. Discussion. Structural stability was an important factor in the discovery of the complex behavior of dynamical systems already in the three-dimensional case; it continues to play a significant role in the modern theory of dynamical systems. Structural stability is of general scientific importance, played a key role in the construction of catastrophe theory, it went beyond the framework of the theory of dynamical systems and mathematics itself, penetrates into other areas of science, including the humanitarian sphere.

Mode transition plays an important role in the operation of hybrid electric vehicles. The clutch is a key actuator for mode transition, but friction resulting from its use makes it difficult to achieve seamless mode transition. Moreover, as is usual in an electromechanical coupling system, the hybrid powertrain may exhibit complex dynamic behaviours as operating parameters change during mode transition. This paper considered changes in the clutch friction coefficient, and established a mathematical model of the hybrid powertrain in a parallel-series hybrid electric vehicle (PSHEV) during mode transition. The Routh-Hurwitz criterion and bifurcation theory are introduced to analyse the influence of speed difference on the dynamic characteristics of the hybrid powertrain, and the corresponding instability threshold were given. Furthermore, an optimised adaptive control methodology was proposed to control the dynamic behaviours, and tests on PSHEV were carried out. The results show that the variations of speed difference may lead to the occurrence of Fold and Hopf bifurcations, and that once the speed difference reaches the instability threshold, it may cause the system to enter a chaotic state and exhibit random oscillation. The proposed control methodology can effectively expand the security domain and suppress the oscillation to improve smoothness of mode transition.