Search Results

This chapter discusses old-fashioned cognitive development from the point of view of two modern approaches, connectionism and nonlinear dynamical systems theory. The main assertion in both connectionist and dynamic systems approaches is that higher cognitive functioning is largely based on nonsymbolic, graded, and dynamic properties, of which these same approaches provide the best account. The chapter argues that the claim concerning nonsymbolic higher order cognition is overstated and explains its position by focusing on sudden transitions in cognitive development.

This chapter describes a fundamental stability theory for nonlinear dynamical systems using vector Lyapunov functions. It first introduces the notation and definitions before developing stability theorems via vector Lyapunov functions for continuous-time and discrete-time nonlinear dynamical systems. It then extends the theory of vector Lyapunov functions by constructing a generalized comparison system whose vector field can be a function of the comparison system states as well as the nonlinear dynamical system states. It also presents a generalized convergence result which, in the case of a scalar comparison system, specializes to the classical Krasovskii–LaSalle theorem. In the analysis of large-scale nonlinear interconnected dynamical systems, several Lyapunov functions arise naturally from the stability properties of each individual subsystem.

This chapter extends the cybernetic perspective to machinic philosophy, evident in Deleuze and Guattari’s concept of the assemblage and its intersections with nonlinear dynamical systems (i.e., “chaos”) theory. It develops more fully the concept of the computational assemblage, specifically in relation to Robert Shaw’s “dripping faucet as a model chaotic system” and Jim Crutchfield’s ∈-machine (re)construction.

This chapter introduces the notion of a control vector Lyapunov function as a generalization of control Lyapunov functions, showing that asymptotic stabilizability of a nonlinear dynamical system is equivalent to the existence of a control vector Lyapunov function. These control vector Lyapunov functions are used to develop a universal decentralized feedback control law for a decentralized nonlinear dynamical system that possesses guaranteed gain and sector margins in each decentralized input channel. The chapter also describes the connections between the notion of vector dissipativity and optimality of the proposed decentralized feedback control law. The proposed control framework is then used to construct decentralized controllers for large-scale nonlinear dynamical systems with robustness guarantees against full modeling uncertainty.

This chapter presents an overview of the subject of artificial smart structures, and introduces the fields of biomimetics and bio-inspired computing. It emphasizes that nonlinear response is the crux of field-tunability of properties, so essential for achieving adaptability in smart structures. The essence of nonlinear response is described here; however, the appendices on nonlinear-dynamical systems and on chaos should be read for a more detailed description. The various causes of nonlinear response of materials are delineated. A distinction is made between smart systems, structures, and materials, as well as between functional materials and smart materials. The importance of scale in the performance characteristics of materials and structures is described. The chapter ends with a brief discussion of what is in store for us in the future. As argued by Moravec, artificial smart structures are on a Darwinian-like evolutionary trajectory, and, assisted by us, their evolution will occur millions of times faster than biological evolution.

This chapter develops a general framework for finite-time stability analysis based on control vector Lyapunov functions. Specifically, it develops a vector comparison system whose solution is finite-time stable and relates this finite-time stability property to the stability properties of a nonlinear dynamical system using a vector comparison principle. The results are specialized to the case of a scalar Lyapunov function to obtain universal finite-time stabilizers for nonlinear systems that are affine in the control. Finally, the utility of the proposed framework is demonstrated using two numerical examples: the first involves a large-scale dynamical system with control signals for each decentralized control channel as a function of time; the second example considers control of thermoacoustic instabilities in combustion processes.

This chapter describes a stability and control design framework for time-varying and time-invariant sets of nonlinear dynamical systems. The framework is applied to the problem of coordination control for multiagent interconnected systems predicated on vector Lyapunov functions. In multiagent systems, several Lyapunov functions arise naturally where each agent can be associated with a generalized energy function corresponding to a component of a vector Lyapunov function. The chapter characterizes a moving formation of vehicles as a time-varying set in the state space to develop a distributed control design framework for multivehicle coordinated motion control by designing stabilizing controllers for time-varying sets of nonlinear dynamical systems. The proposed cooperative control algorithms are shown to globally exponentially stabilize both moving and static formations.

This introduction charts out the topics to come in the book, describing the advantages and indeed the necessity of nonlinear dynamical systems (NDS) approaches to knowledge. It argues that a paradigm shift is occurring in the social sciences, one that is especially vital for the individual and societal dilemmas we are experiencing today. The editors provide preliminary examples and explanations of chaos, dynamics, and nonlinearity. The introduction lays out our first approach to the book’s six organizing themes and makes suggestions about how readers with varying levels of exposure to NDS can approach the rest of the book, discusses the volume’s structure and how to use the comments from the editors, and finally summarizes the chapters.

This chapter pulls together this volume’s interests in “wicked problems” and its emphasis on examining hierarchical and nested systems processes. It returns to the six themes for a final integration, tracing stages of how to become familiar with nonlinear dynamical systems (NDS), the signs and meanings of nonlinearity, and how one can “level up” and “level down” to gain insight into systems of interest. Patterning is discussed, with an emphasis on the profound meanings of fractals. The COVID-19 pandemic is used as an example throughout. The chapter emphasizes again the ideas of a changing worldview and argues as well for a humble approach to living and improving our human lives in the systems that compose us, that we contribute to, and that we wish to change.

When considering attentional abilities, two physiological variables need to be recorded: basal (tonic) activity or event-related (phasic) activity. In general, tonic activity can be derived from the ongoing level of activity in the system when the organism is at rest. The length of time needed to assess tonic level appropriately will differ across physiological systems, but in many cases it will be on the order of several minutes. Phasic responses typically are measured over time periods that capture the full response from basal level until the physiological parameter returns to its basal level. Decisions about how to assess changes in physiology are somewhat more difficult than those for assessing tonic levels of activity. This chapter discusses several methods used for assessing change and some of the advantages and disadvantages associated with each measure. The use of Fourier analysis or fast Fourier transform, wavelet analysis, and nonlinear dynamical systems analysis for assessing global aspects of physiological signals are also considered.

This chapter addresses protocell research from the perspective of nonlinear chemical dynamical systems. It assumes that early cell ancestors were formed before the genetic code for protein synthesis and before RNA and DNA emerged.