Nonlinear Dynamics in Human Behavior

In this volume, first we formulate a framework of fuzzy types to represent both partial truth and uncertainty about concept and relation types in conceptual graphs. Like fuzzy attribute values, fuzzy types also form a lattice laying a common ground for lattice-based computation of fuzzy granules. Second, for automated reasoning with fuzzy conceptual graphs, we develop foundations of order-sorted fuzzy set logic programming, extending the theory of annotated logic programs of Kifer and Subrahmanian (1992). Third, we show some recent applications of fuzzy conceptual graphs to modelling and computing with generally quantified statements, approximate knowledge retrieval, and natural language query understanding. Dynamical Systems in One and Two Dimensions: A Geometrical Approach 1 One-Dimensional Dynamical Systems 1 Linear Systems 2 Nonlinear Systems: First Steps 4 Potential Functions 6 Bifurcation Types 9 Two-Dimensional Systems 14 Linear Systems and their Classification 14 Nonlinear Systems 20 Limit Cycles 22 Hopf Bifurcation 23 Potential Functions in Two-Dimensional Systems 25 Oscillators 27 Benefits and Pitfalls in Analyzing Noise in Dynamical Systems – On Stochastic Differential Equations and System Identification 1 Introduction 1 Probability 2 Mean and Expectation Values 3 Probability Distribution and Density 3 Dynamics and Noise 5 Stochastic Dynamics 5 Time-Dependent Probability Density Functions 8 Example: The HKB-Model 9 Spurious Drift in the Amplitude Dynamics of a Limit Cycle Oscillator 11 Periodically Forced Potentials – Stochastic Resonance and More 13 System Identification 15 Drift and Diffusion Coefficients 16 Markov Properties and the Chapman-Kolmogorov Test 18 Rhythmic Movements 19 HKB-Bifurcation – Real Data 20 Posture – Center-of-Pressure Dynamics 21 Summary 23 References 24 The Dynamical Organization of Limb Movements 1 Introduction 1 The Birth of the Dynamical Perspective 2 The Empirical Study of Rhythmic Movements as Limit Cycles 5 Rhythmic Movements under Precision Requirements 8 Perspectives Incorporating Discrete Movements 10 Phase Flows and Topologies 11 In Conclusion 16 References 18 Perspectives on the Dynamic Nature of Coupling in Human Coordination 1 Introduction 1 Coordination Depends on Intrinsic Dynamics and Coupling 4 Effect of the Coupling 5 Effect of the Intrinsic Dynamics 6 Extracting Principles Underlying the Formation of Coordinative Patterns: Convergence and Divergence 13 Experimental Evidence for Convergence/Divergence in Perception–Action 14 Formalization of Convergence/Divergence in the State Space 16 Conclusions 22 References 22 Do We Need Internal Models for Movement Control? 1 Dynamical Systems Theory 1 Positional Control and Equilibrium Point Theory 4 Force Control and Computational Theory 7 Mapping between Movements and Control Signals 11 Internal Models versus Look Up Tables 15 Conclusion 18 References 18 Nonlinear Dynamics in Speech Perception 1 Introduction 1 Nonlinearity 2 Context Sensitivity 4 Stability and Flexibility 5 Dynamics of Vowel Perception and Imitation 7 Dynamics of Consonant Perception: English and French 9 References 14 A Neural Basis for Perceptual Dynamics 1 Perceptual Stability: Natural or Otherwise 2 Neural Stabilization 4 The Biophysical Basis of Neural Stabilization 5 The Time Scale 5 The Core Dynamical Concept 6 Stable Activation States in the Absence of Stimulation 6 Response to Stimulation 8 Perceptual Thresholds, Perceptual Stability and Uncertainty 10 The Stabilization of Activation within Detector Ensembles 11 Neural Connectivity 11 Interaction 12 Interaction within Detector Ensembles 12 Detection Instability 13 Stabilization of Activation within Detector Ensembles 14 Removing the Stimulus 15 Perceptual Selection 15 Perceptual Bistability 15 Rates of Change in Activation 18 Perceptual Selection of the Favored Stimulus Alternative 19 Perceptual Selection of the Unfavored Stimulus Alternative 20 Objects and Feature Integration 20 The Signature Features of Perceptual Dynamics 22 Spontaneous Switching 22 Hysteresis 23 Conclusion 24 References 25 Optical Illusions: Examples for Nonlinear Dynamics in Perception* 1 Ambiguous Figures 1 The Verbal Transformation Effect 4 3D Vision and Autostereograms 5 Perception of Motion, Colour and Brightness 8 The Leaning Tower of Pisa Illusion 8 References 12 A Dynamical Systems Approach to Musical Tonality* 1 Introduction 1 Tonality 2 A Dynamical Systems Approach 5 Predicting Tonality 8 Discussion 15 References 17 Cover 1 Front Matter 2 Dynamical Systems in One and Two Dimensions: A Geometrical Approach 8 One-Dimensional Dynamical Systems 8 Linear Systems 9 Nonlinear Systems: First Steps 11 Potential Functions 13 Bifurcation Types 16 Two-Dimensional Systems 21 Linear Systems and their Classification 21 Nonlinear Systems 27 Limit Cycles 29 Hopf Bifurcation 30 Potential Functions in Two-Dimensional Systems 32 Oscillators 34 Benefits and Pitfalls in Analyzing Noise in Dynamical Systems – On Stochastic Differential Equations and System Identification 41 Introduction 41 Probability 42 Probability Distribution and Density 43 Mean and Expectation Values 43 Dynamics and Noise 45 Stochastic Dynamics 45 Time-Dependent Probability Density Functions 48 Example: The HKB-Model 49 Spurious Drift in the Amplitude Dynamics of a Limit Cycle Oscillator 51 Periodically Forced Potentials – Stochastic Resonance and More 53 System Identification 55 Drift and Diffusion Coefficients 56 Markov Properties and the Chapman-Kolmogorov Test 58 Rhythmic Movements 59 HKB-Bifurcation – Real Data 60 Posture – Center-of-Pressure Dynamics 61 Summary 63 References 64 The Dynamical Organization of Limb Movements 75 Introduction 75 The Birth of the Dynamical Perspective 76 The Empirical Study of Rhythmic Movements as Limit Cycles 79 Rhythmic Movements under Precision Requirements 82 Perspectives Incorporating Discrete Movements 84 Phase Flows and Topologies 85 In Conclusion 90 References 92 Perspectives on the Dynamic Nature of Coupling in Human Coordination 97 Introduction 97 Coordination Depends on Intrinsic Dynamics and Coupling 100 Effect of the Coupling 101 Effect of the Intrinsic Dynamics 102 Extracting Principles Underlying the Formation of Coordinative Patterns: Convergence and Divergence 109 Experimental Evidence for Convergence/Divergence in Perception–Action 110 Formalization of Convergence/Divergence in the State Space 112 References 118 Conclusions 118 Do We Need Internal Models for Movement Control? 121 Dynamical Systems Theory 121 Positional Control and Equilibrium Point Theory 124 Force Control and Computational Theory 127 Mapping between Movements and Control Signals 131 Internal Models versus Look Up Tables 135 Conclusion 138 References 138 Nonlinear Dynamics in Speech Perception 141 Introduction 141 Nonlinearity 142 Context Sensitivity 144 Stability and Flexibility 145 Dynamics of Vowel Perception and Imitation 147 Dynamics of Consonant Perception: English and French 149 References 154 A Neural Basis for Perceptual Dynamics 157 Perceptual Stability: Natural or Otherwise 158 Neural Stabilization 160 The Time Scale 161 The Biophysical Basis of Neural Stabilization 161 Stable Activation States in the Absence of Stimulation 162 The Core Dynamical Concept 162 Response to Stimulation 164 Perceptual Thresholds, Perceptual Stability and Uncertainty 166 The Stabilization of Activation within Detector Ensembles 167 Neural Connectivity 167 Interaction within Detector Ensembles 168 Interaction 168 Detection Instability 169 Stabilization of Activation within Detector Ensembles 170 Perceptual Selection 171 Removing the Stimulus 171 Perceptual Bistability 171 Rates of Change in Activation 174 Perceptual Selection of the Favored Stimulus Alternative 175 Objects and Feature Integration 176 Perceptual Selection of the Unfavored Stimulus Alternative 176 The Signature Features of Perceptual Dynamics 178 Spontaneous Switching 178 Hysteresis 179 Conclusion 180 References 181 Optical Illusions: Examples for Nonlinear Dynamics in Perception* 184 Ambiguous Figures 184 The Verbal Transformation Effect 187 3D Vision and Autostereograms 188 Perception of Motion, Colour and Brightness 191 The Leaning Tower of Pisa Illusion 191 References 195 A Dynamical Systems Approach to Musical Tonality* 197 Introduction 197 Tonality 198 A Dynamical Systems Approach 201 Predicting Tonality 204 Discussion 211 References 213 Back Matter 216 Cover......Page 1 Front Matter......Page 2 The Verbal Transformation Effect......Page 4 Stable Activation States in the Absence of Stimulation......Page 6 Linear Systems......Page 9 Stabilization of Activation within Detector Ensembles......Page 14 Objects and Feature Integration......Page 20 Spontaneous Switching......Page 22 Hysteresis......Page 23 References......Page 25 Nonlinear Systems......Page 27 Probability Distribution and Density......Page 3 A Dynamical Systems Approach......Page 5 One-Dimensional Dynamical Systems......Page 8 Nonlinear Systems: First Steps......Page 11 Potential Functions......Page 13 Discussion......Page 15 Bifurcation Types......Page 16 Rates of Change in Activation......Page 18 Perceptual Selection of the Favored Stimulus Alternative......Page 19 Linear Systems and their Classification......Page 21 Conclusion......Page 24 Perceptual Thresholds, Perceptual Stability and Uncertainty......Page 10 Dynamics of Vowel Perception and Imitation......Page 7 References......Page 12 References......Page 17 Limit Cycles......Page 29 Hopf Bifurcation......Page 30 Potential Functions in Two-Dimensional Systems......Page 32 Oscillators......Page 34 Introduction......Page 41 Probability......Page 42 Mean and Expectation Values......Page 43 Stochastic Dynamics......Page 45 Time-Dependent Probability Density Functions......Page 48 Example: The HKB-Model......Page 49 Spurious Drift in the Amplitude Dynamics of a Limit Cycle Oscillator......Page 51 Periodically Forced Potentials – Stochastic Resonance and More......Page 53 System Identification......Page 55 Drift and Diffusion Coefficients......Page 56 Markov Properties and the Chapman-Kolmogorov Test......Page 58 Rhythmic Movements......Page 59 HKB-Bifurcation – Real Data......Page 60 Posture – Center-of-Pressure Dynamics......Page 61 Summary......Page 63 References......Page 64 Introduction......Page 75 The Birth of the Dynamical Perspective......Page 76 The Empirical Study of Rhythmic Movements as Limit Cycles......Page 79 Rhythmic Movements under Precision Requirements......Page 82 Perspectives Incorporating Discrete Movements......Page 84 Phase Flows and Topologies......Page 85 In Conclusion......Page 90 References......Page 92 Introduction......Page 97 Coordination Depends on Intrinsic Dynamics and Coupling......Page 100 Effect of the Coupling......Page 101 Effect of the Intrinsic Dynamics......Page 102 Extracting Principles Underlying the Formation of Coordinative Patterns: Convergence and Divergence......Page 109 Experimental Evidence for Convergence/Divergence in Perception–Action......Page 110 Formalization of Convergence/Divergence in the State Space......Page 112 Conclusions......Page 118 Dynamical Systems Theory......Page 121 Positional Control and Equilibrium Point Theory......Page 124 Force Control and Computational Theory......Page 127 Mapping between Movements and Control Signals......Page 131 Internal Models versus Look Up Tables......Page 135 References......Page 138 Introduction......Page 141 Nonlinearity......Page 142 Context Sensitivity......Page 144 Stability and Flexibility......Page 145 Dynamics of Vowel Perception and Imitation......Page 147 Dynamics of Consonant Perception: English and French......Page 149 References......Page 154 A Neural Basis for Perceptual Dynamics......Page 157 Perceptual Stability: Natural or Otherwise......Page 158 Neural Stabilization......Page 160 The Biophysical Basis of Neural Stabilization......Page 161 The Core Dynamical Concept......Page 162 Response to Stimulation......Page 164 Perceptual Thresholds, Perceptual Stability and Uncertainty......Page 166 Neural Connectivity......Page 167 Interaction......Page 168 Detection Instability......Page 169 Stabilization of Activation within Detector Ensembles......Page 170 Perceptual Bistability......Page 171 Rates of Change in Activation......Page 174 Perceptual Selection of the Favored Stimulus Alternative......Page 175 Perceptual Selection of the Unfavored Stimulus Alternative......Page 176 Spontaneous Switching......Page 178 Hysteresis......Page 179 Conclusion......Page 180 References......Page 181 Ambiguous Figures......Page 184 The Verbal Transformation Effect......Page 187 3D Vision and Autostereograms......Page 188 The Leaning Tower of Pisa Illusion......Page 191 References......Page 195 Introduction......Page 197 Tonality......Page 198 A Dynamical Systems Approach......Page 201 Predicting Tonality......Page 204 Discussion......Page 211 References......Page 213 Back Matter......Page 216 Humans engage in a seemingly endless variety of different behaviors, of which some are found across species, while others are conceived of as typically human. Most generally, behavior comes about through the interplay of various constraints – informational, mechanical, neural, metabolic, and so on – operating at multiple scales in space and time. Over the years, consensus has grown in the research community that, rather than investigating behavior only from bottom up, it may be also well understood in terms of concepts and laws on the phenomenological level. Such top down approach is rooted in theories of synergetics and self-organization using tools from nonlinear dynamics. The present compendium brings together scientists from all over the world that have contributed to the development of their respective fields departing from this background. It provides an introduction to deterministic as well as stochastic dynamical systems and contains applications to motor control and coordination, visual perception and illusion, as well as auditory perception in the context of speech and music.