Cover
S Title
Mathematical Approaches to Biological Systems
Copyright
© Springer Japan 2015
ISBN 978-4-431-55443-1
ISBN 978-4-431-55444-8 (eBook)
DOI 10.1007/978-4-431-55444-8
Library of Congress Control Number: 2015935193
Preface
Contents
1 Human Balance Control: Dead Zones, Intermittency, and Micro-chaos
1.1 Introduction
1.2 Historical Background
1.2.1 An Ecological Example
1.2.2 Micro-chaos
1.3 Human Postural Sway
1.4 Stabilizing the Upright Position
1.4.1 First-Order Models
1.4.2 Propagation of Threshold Effects
1.4.3 Transient Stabilization
1.5 Stick Balancing at the Fingertip
1.6 Dead Zone Benefits
1.7 Concluding Remarks
References
2 Dynamical Robustness of Complex Biological Networks
2.1 Network Robustness
2.2 Coupled Oscillator Networks
2.2.1 Globally Coupled Networks
2.2.2 Homogeneously Coupled Networks
2.2.3 Heterogeneously Coupled Networks
Random Inactivation
Targeted Inactivation
Weighted Coupling
Heterogeneity of Oscillator Units
2.2.4 Other Network Structures
2.3 Application to Biological Networks
2.3.1 A Neuronal Network Model
2.3.2 Robustness of Firing Activity
Inactivation of Neurons
Targeted Inactivation
Effects of Chemical Synapses
2.4 Summary
References
3 Hardware-Oriented Neuron Modeling Approach by Reconfigurable Asynchronous Cellar Automaton
3.1 Introduction
3.2 Concepts of Asynchronous Sequential Logic Neuron Model
3.3 Examples of the Asynchronous Sequential Logic Neuron Models
3.4 Bifurcation Analysis and On-Chip Learning of the Fourth-Generation Model
3.5 Future Plans and Potential Applications
3.6 Conclusions
References
4 Entrainment Limit of Weakly Forced Nonlinear Oscillators
4.1 Introduction
4.2 Entrainment Modeled by the Phase Equation
4.3 Entrainment Design Under Practical Constrains
4.4 Fundamental Limits of Entrainment
4.4.1 1:1 Entrainment for 1
4.4.2 1:1 Entrainment for p=1 and p=8
4.4.3 General m:n Entrainment
4.5 An Example of Efficient Injection Locking: The Hodgkin–Huxley Neuron Model
4.6 Conclusion and Discussion
Appendix 1 Assumptions on the Phase Response Function and Outlines of the Presented Proofs
Appendix 2 Derivation of the Nonlinear Equations Determining Optimal Forcings
Appendix 3 Detailed Information Regarding Optimal Forcings
Appendix 4 Derivation of Optimal Forcings in Two Limits
References
5 A Universal Mechanism of Determining the Robustness of Evolving Systems
5.1 Introduction
5.2 A Simple Model of the Transition in Robustness of Open Systems
5.2.1 The Model
5.2.2 Transition in the Growth Behavior
Transition in Network Topology at Between m=4 and 5
The Novel Transition
5.3 A Mean-Field Approach for the Transition
5.3.1 Fitness Distribution Function and the Convolution-and-Cut Process
5.3.2 Determination of the Transition Point
5.3.3 Negative Drift During the Link-Deletion Event
5.3.4 Analytical Approach for the Estimation of E
Convolution Without Drift
Calculating Older Generations
5.3.5 Analytical Estimation of E Using Fokker-Plank Equation
Solution for Neutral Diffusion Process
Solution for the System with Negative Drift
5.3.6 Numerical Calculation of E
5.4 Discussion
References
6 Switching of Primarily Relied Information by Ants: A Combinatorial Study of Experiment and Modeling
6.1 Introduction
6.2 Experiment for the Foraging Path Selection by Ants
6.2.1 Preparation
6.2.2 Measurement
6.3 Qualitative Analysis of Experiment
6.4 Model
6.4.1 Basic Setup
6.4.2 Walking Rule
6.4.3 Time Development of Pheromone Field
6.4.4 Initial Condition and Values of Parameters
6.4.5 Simulation and Analysis
6.5 Conclusion and Perspectives
References
7 Chases and Escapes: From Singles to Groups
7.1 Introduction
7.2 Simple Chase-and-Escape Problems
7.3 Theories of Collective Motions
7.3.1 Vicsek Model
7.3.2 Optimal Velocity Model
7.4 Group Chase and Escape
7.4.1 Basic Model
7.4.2 Simulation Results
Lifetimes of Targets
7.4.3 Quantitative Analysis of Catching Process
7.4.4 Extensions
Issues of Range of Each Chaser
Issues of Long-Range Chaser Doping
Issues of Hopping Fluctuations
7.5 Recent Developments on Group Chase and Escape
7.5.1 Reactions
7.5.2 Motions
7.6 Discussion
References
