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This book presents a unique fusion of two different research
topics. One is related to the traditional mathematical problem of
chases and escapes. The problem mainly deals with a situation where
a chaser pursues an evader to analyze their trajectories and
capture time. It dates back more than 300 years and has developed
in various directions such as differential games. The other topic
is the recently developing field of collective behavior, which
investigates origins and properties of emergent behavior in groups
of self-driving units. Applications include schools of fish, flocks
of birds, and traffic jams. This book first reviews representative
topics, both old and new, from these two areas. Then it presents
the combined research topic of "group chase and escape", recently
proposed by the authors. Although the combination is simple and
straightforward, the book describes the emergence of rather
intricate behavior, provoking the interest of readers for further
developments and applications of related topics.
This book presents a unique fusion of two different research
topics. One is related to the traditional mathematical problem of
chases and escapes. The problem mainly deals with a situation where
a chaser pursues an evader to analyze their trajectories and
capture time. It dates back more than 300 years and has developed
in various directions such as differential games. The other topic
is the recently developing field of collective behavior, which
investigates origins and properties of emergent behavior in groups
of self-driving units. Applications include schools of fish, flocks
of birds, and traffic jams. This book first reviews representative
topics, both old and new, from these two areas. Then it presents
the combined research topic of "group chase and escape", recently
proposed by the authors. Although the combination is simple and
straightforward, the book describes the emergence of rather
intricate behavior, provoking the interest of readers for further
developments and applications of related topics.
This book presents the most recent mathematical approaches to the
growing research area of networks, oscillations, and collective
motions in the context of biological systems. Bringing together the
results of multiple studies of different biological systems, this
book sheds light on the relations among these research themes.
Included in this book are the following topics: feedback systems
with time delay and threshold of sensing (dead zone), robustness of
biological networks from the point of view of dynamical systems,
the hardware-oriented neuron modeling approach, a universal
mechanism governing the entrainment limit under weak forcing, the
robustness mechanism of open complex systems, situation-dependent
switching of the cues primarily relied on by foraging ants, and
group chase and escape. Research on different biological systems is
presented together, not separated by specializations or by model
systems. Therefore, the book provides diverse perspectives at the
forefront of current mathematical research on biological systems,
especially focused on networks, oscillations, and collective
motions. This work is aimed at advanced undergraduate, graduate,
and postdoctoral students, as well as scientists and engineers. It
will also be of great use for professionals in industries and
service sectors owing to the applicability of topics such as
networks and synchronizations.
The second edition of Mathematics as a Laboratory Tool reflects the
growing impact that computational science is having on the career
choices made by undergraduate science and engineering students. The
focus is on dynamics and the effects of time delays and stochastic
perturbations ("noise") on the regulation provided by feedback
control systems. The concepts are illustrated with applications to
gene regulatory networks, motor control, neuroscience and
population biology. The presentation in the first edition has been
extended to include discussions of neuronal excitability and
bursting, multistability, microchaos, Bayesian inference,
second-order delay differential equations, and the
semi-discretization method for the numerical integration of delay
differential equations. Every effort has been made to ensure that
the material is accessible to those with a background in calculus.
The text provides advanced mathematical concepts such as the
Laplace and Fourier integral transforms in the form of Tools.
Bayesian inference is introduced using a number of detective-type
scenarios including the Monty Hall problem.
This introductory textbook is based on the premise that the
foundation of good science is good data. The educational challenge
addressed by this introductory textbook is how to present a
sampling of the wide range of mathematical tools available for
laboratory research to well-motivated students with a mathematical
background limited to an introductory course in calculus.
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