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Many nonlinear systems around us can generate a very complex and counter-intuitive dynamics that contrasts with their simplicity, but their understanding requires concepts that are outside the basic training of most science students. This textbook, which is the fruit of graduate courses that the authors have taught at their respective universities, provides a richly illustrated introduction to nonlinear dynamical systems and chaos and a solid foundation for this fascinating subject. It will satisfy those who want discover this field, including at the undergraduate level, but also those who need a compact and consistent overview, gathering the concepts essential to nonlinear scientists.The first and second chapters describe the essential concepts needed to describe nonlinear dynamical systems as well as their stability. The third chapter introduces the concept of bifurcation, where the qualitative dynamical behavior of a system changes. The fourth chapter deals with oscillations, from their birth to their destabilization, and how they respond to external driving. The fifth and sixth chapters discuss complex behaviors that only occur in state spaces of dimension three and higher: quasi-periodicity and chaos, from their general properties to quantitative methods of characterization. All chapters are supplemented by exercises ranging from direct applications of the notions introduced in the corresponding chapter to elaborate problems involving concepts from different chapters, as well as numerical explorations.

Dynamics. --- Bifurcation. --- Chaos Theory. --- Dynamic System. --- Nonlinear Dynamics. --- Strange Attractor.

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In its second expanded and updated edition, this textbook covers the theory and applications of dynamical processes whose time evolution is not continuous, but rather is modeled in discrete time steps through difference equations. These discrete models play an increasingly important role - reinforced by the use of computers - in science, engineering and economics. This new edition also covers special applications in financial mathematics. Following a basic introduction with examples, the first part provides a thorough survey of linear systems and their stability properties.The second part deals with nonlinear systems, especially their stability, and includes an excursus on chaos and fractals and an introduction into the more recent theory of positive dynamical systems along with applications in biology and economics. In seiner zweiten erweiterten und aktualisierten Auflage befasst sich dieses Lehrbuch mit der Theorie und den Anwendungen von dynamischen Prozessen, deren zeitliche Entwicklung nicht kontinuierlich, sondern in diskreten Zeitschritten durch Differenzengleichungen modelliert wird. Verstärkt noch durch den Einsatz von Computern spielen die diskreten Modelle eine zunehmend wichtige Rolle in den Natur-, Ingenieur- und Wirtschaftswissenschaften. Daher werden in dieser Neuauflage zusätzlich auch Anwendungen in der Finanzmathematik betrachtet. Nach einer grundlegenden Einführung mit Beispielen werden im ersten Teil lineare Systeme und ihre Stabilitätseigenschaften gründlich behandelt. Der zweite Teil befasst sich mit nichtlinearen Systemen, insbesondere deren Stabilität, und enthält einen Exkurs zu Chaos und Fraktalen sowie eine Einführung in die neuere Theorie positiver dynamischer Systeme nebst Anwendungen in Biologie und Ökonomie.

Difference equations. --- Dynamics --- Data processing. --- Difference Equation. --- Discreet System. --- Dynamic System. --- Financial Mathematics.

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This book appeals to scientists, teachers and graduate students in mathematics, and will be of interest for scholars in applied sciences as well, in particular in medicine, biology and social sciences. The models in this connection apply, in particular, to the study of the immune system response and to the predator–prey dynamic. The efficiency of public transport is also considered and blast waves in explosions are studied. Other contributions concern pure mathematics, in particular Pythagorean means, sequences of matrices and Markov chains, and these give evidence of deep links with Symmetry.

paradox of enrichment --- prey–predator system --- persistence of predators --- extinction of predators --- blast waves --- non-ideal gas --- Rankine–Hugoniot conditions --- magnetogasdynamics --- dynamic model --- immune system response --- immune cells --- abnormal cells --- nonlinear ordinary differential equations --- stability --- diet --- Aggregation dynamic system --- Discrete system --- Epidemic model --- Cauchy’s interlacing theorem --- Output-feedback control --- Stability --- Antistable/Stable matrix --- onboard comfort level --- Markow chain --- bus passenger occupancy prediction --- Chebyshev inequality --- Tracy-Singh product --- continuous field of operators --- Bochner integral --- weighted Pythagorean mean

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Party competition for votes in free and fair elections involves complex interactions by multiple actors in political landscapes that are continuously evolving, yet classical theoretical approaches to the subject leave many important questions unanswered. Here Michael Laver and Ernest Sergenti offer the first comprehensive treatment of party competition using the computational techniques of agent-based modeling. This exciting new technology enables researchers to model competition between several different political parties for the support of voters with widely varying preferences on many different issues. Laver and Sergenti model party competition as a true dynamic process in which political parties rise and fall, a process where different politicians attack the same political problem in very different ways, and where today's political actors, lacking perfect information about the potential consequences of their choices, must constantly adapt their behavior to yesterday's political outcomes. Party Competition shows how agent-based modeling can be used to accurately reflect how political systems really work. It demonstrates that politicians who are satisfied with relatively modest vote shares often do better at winning votes than rivals who search ceaselessly for higher shares of the vote. It reveals that politicians who pay close attention to their personal preferences when setting party policy often have more success than opponents who focus solely on the preferences of voters, that some politicians have idiosyncratic "valence" advantages that enhance their electability--and much more.

Competition --- Political parties. --- Competition (Economics) --- Competitiveness (Economics) --- Economic competition --- Commerce --- Conglomerate corporations --- Covenants not to compete --- Industrial concentration --- Monopolies --- Open price system --- Supply and demand --- Trusts, Industrial --- Parties, Political --- Party systems, Political --- Political party systems --- Political science --- Divided government --- Intra-party disagreements (Political parties) --- Political conventions --- Political aspects --- Simulation methods. --- Economic aspects --- Monte Carlo parameterization. --- Robert Axelrod. --- Voronoi tessellations. --- agent-based model. --- agent-based modeling. --- agent-based models. --- competition. --- competitive spatial location. --- computational geometry. --- computer simulation. --- decision rules. --- decisions rules. --- dynamic multiparty competition. --- dynamic system. --- grid sweeping. --- multiparty competition. --- party competition. --- party leaders. --- party policy. --- policy preferences. --- political parties. --- political party. --- political systems. --- politicians. --- postwar democracy. --- spatial models. --- stochastic processes. --- valence models. --- vote-seeking rules. --- voter behavior. --- voter preferences. --- votes. --- Political sociology --- Political parties

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The advent of Internet of Things offers a scalable and seamless connection of physical objects, including human beings and devices. This, along with artificial intelligence, has moved transportation towards becoming intelligent transportation. This book is a collection of eleven articles that have served as examples of the success of internet of things and artificial intelligence deployment in transportation research. Topics include collision avoidance for surface ships, indoor localization, vehicle authentication, traffic signal control, path-planning of unmanned ships, driver drowsiness and stress detection, vehicle density estimation, maritime vessel flow forecast, and vehicle license plate recognition. High-performance computing services have become more affordable in recent years, which triggered the adoption of deep-learning-based approaches to increase the performance standards of artificial intelligence models. Nevertheless, it has been pointed out by various researchers that traditional shallow-learning-based approaches usually have an advantage in applications with small datasets. The book can provide information to government officials, researchers, and practitioners. In each article, the authors have summarized the limitations of existing works and offered valuable information on future research directions.

decision-making --- autonomous navigation --- collision avoidance --- scene division --- deep reinforcement learning --- maritime autonomous surface ships --- internet of things --- crowdsourcing --- indoor localization --- data fusion --- security --- authentication --- Inertial Measurement Units --- road transportation --- traffic signal control --- speed guidance --- vehicle arrival time --- connected vehicle --- unmanned ships --- DDPG --- autonomous path planning --- end-to-end --- at-risk driving --- deep support vector machine --- driver drowsiness --- driver stress --- multi-objective genetic algorithm --- multiple kernel learning --- urban freeway --- hybrid dynamic system --- state transition --- unknown inputs observer --- vehicle density --- maritime vessel flows --- intelligent transportation systems --- deep learning --- automatic license plate recognition --- intelligent vehicle access --- histogram of oriented gradients --- artificial neural networks --- convolutional neural networks --- time-frequency --- Inertial Measurement Unit (IMU) --- road anomalies --- n/a