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Équations différentielles non linéaires. --- Differential equations, Nonlinear. --- Cycles limites. --- Limit cycles. --- Equations differentielles ordinaires --- Theorie qualitative --- Equations differentielles ordinaires --- Theorie qualitative

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Dynamical system theory has developed rapidly over the past fifty years. It is a subject upon which the theory of limit cycles has a significant impact for both theoretical advances and practical solutions to problems. Hopf bifurcation from a center or a focus  is integral to the theory of bifurcation of limit cycles, for which normal form theory is a central tool. Although Hopf bifurcation has been studied for more than half a century, and normal form theory for over 100 years, efficient computation in this area is still a challenge with implications for Hilbert’s 16th problem. This book introduces the most recent developments in this field and provides major advances in fundamental theory of limit cycles. Split into two parts, the first focuses on  the study of limit cycles bifurcating from Hopf singularity using normal form theory with later application to Hilbert’s 16th problem, while the second considers near Hamiltonian systems using Melnikov function as the main mathematical tool. Classic topics with new results are presented in a clear and concise manner and are accompanied by the liberal use of illustrations throughout. Containing a wealth of examples and structured algorithms that are treated in detail, a good balance between theoretical and applied topics is demonstrated. By including complete Maple programs within the text, this book also enables the reader to reconstruct the majority of formulas provided, facilitating the use of concrete models for study. Through the adoption of an elementary and practical approach, this book will be of use to graduate mathematics students wishing to study the theory of limit cycles as well as scientists, across a number of disciplines, with an interest in the applications of periodic behavior.

Limit cycles. --- Nonlinear systems. --- Limit cycles --- Bifurcation theory --- Normal forms (Mathematics) --- Nonlinear systems --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory --- Calculus --- Systems, Nonlinear --- Cycles, Limit --- Differential equations --- Limit cycles of differential equations --- Mathematics. --- Approximation theory. --- Dynamics. --- Ergodic theory. --- Differential equations. --- Computer software. --- Statistical physics. --- Dynamical Systems and Ergodic Theory. --- Approximations and Expansions. --- Ordinary Differential Equations. --- Mathematical Software. --- Nonlinear Dynamics. --- Physics --- Mathematical statistics --- Software, Computer --- Computer systems --- 517.91 Differential equations --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Math --- Science --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Statistical methods --- System theory --- Differentiable dynamical systems --- Differentiable dynamical systems. --- Differential Equations. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Global analysis (Mathematics) --- Topological dynamics

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This textbook contains the lecture series originally delivered at the "Advanced Course on Limit Cycles of Differential Equations" in the Centre de Recerca Matemàtica Barcelona in 2006. The topics covered are the center-focus problem for polynomial vector fields, and the application of abelian integrals to limit cycle bifurcations. Both topics are related to Hilbert's sixteenth problem. In particular, the book will be of interest to students and researchers working in the qualitative theory of dynamical systems.

Mathematics. --- Dynamics. --- Ergodic theory. --- Differential equations. --- Ordinary Differential Equations. --- Dynamical Systems and Ergodic Theory. --- Differential Equations. --- Differentiable dynamical systems. --- 517.91 Differential equations --- Differential equations --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Global analysis (Mathematics) --- Topological dynamics --- Limit cycles. --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics

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Recent trends in vehicle engineering are testament to the great efforts that scientists and industries have made to seek solutions to enhance both the performance and safety of vehicular systems. This Special Issue aims to contribute to the study of modern vehicle dynamics, attracting recent experimental and in-simulation advances that are the basis for current technological growth and future mobility. The area involves research, studies, and projects derived from vehicle dynamics that aim to enhance vehicle performance in terms of handling, comfort, and adherence, and to examine safety optimization in the emerging contexts of smart, connected, and autonomous driving.This Special Issue focuses on new findings in the following topics:(1) Experimental and modelling activities that aim to investigate interaction phenomena from the macroscale, analyzing vehicle data, to the microscale, accounting for local contact mechanics; (2) Control strategies focused on vehicle performance enhancement, in terms of handling/grip, comfort and safety for passengers, motorsports, and future mobility scenarios; (3) Innovative technologies to improve the safety and performance of the vehicle and its subsystems; (4) Identification of vehicle and tire/wheel model parameters and status with innovative methodologies and algorithms; (5) Implementation of real-time software, logics, and models in onboard architectures and driving simulators; (6) Studies and analyses oriented toward the correlation among the factors affecting vehicle performance and safety; (7) Application use cases in road and off-road vehicles, e-bikes, motorcycles, buses, trucks, etc.

Technology: general issues --- History of engineering & technology --- tire model parameters identification --- artificial neural networks --- curve fitting --- Pacejka’s magic formula --- intelligent vehicles --- autonomous vehicles --- microscopic traffic simulation --- autonomous driving --- friction estimate --- tire-based control --- ADAS --- potential friction --- energy consumption and recovery --- transmission layouts --- fuel-cell electric vehicles --- adhesion enhancement --- dimple model --- patterned surfaces --- viscoelasticity --- enhancement --- articulated vehicles --- stability analysis --- nonlinear dynamic model --- snake instability --- eigenvalue analysis --- central control --- non-linear model-based predictive control --- pitch behavior --- predictive control --- roll behavior --- self-steering behavior --- vehicle dynamics --- viscoelastic modulus --- rubber --- friction --- empirical modeling --- autonomous emergency steering --- multi-input multi-output model predictive control --- actuator dynamics --- control allocation --- handling enhancement --- road friction --- wear --- tyre --- suspension --- semi-active --- handling --- comfort --- optimisation --- directional stability --- road profile --- road unevenness --- vehicle-road interaction --- vertical vehicle excitation --- tire models --- tire tread --- motorcycle --- rider --- screw axis --- weave --- wobble --- multibody --- gravel pavement --- roughness --- straightedge --- power spectral density --- international roughness index --- vehicle response --- driving comfort --- sky-hook --- in-wheel motor --- semi-active suspension --- quarter-car model --- suspension performance --- suspension test bench --- vehicle stability --- road models --- quarter car models --- limit cycles --- acceleration speed portraits --- speed oscillations --- velocity bifurcations --- noisy limit cycles --- limit flows of trajectories --- Sommerfeld effects --- differential-algebraic systems --- polar coordinates of roads --- covariance equations --- stability in mean --- supercritical speeds --- analytical travel speed amplitudes --- Floquet theory applied to limit cycles --- non-pneumatic tire --- finite element analysis --- steady state analysis --- tire characterization --- footprint --- contact patch --- longitudinal interaction --- n/a --- Pacejka's magic formula

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Recent trends in vehicle engineering are testament to the great efforts that scientists and industries have made to seek solutions to enhance both the performance and safety of vehicular systems. This Special Issue aims to contribute to the study of modern vehicle dynamics, attracting recent experimental and in-simulation advances that are the basis for current technological growth and future mobility. The area involves research, studies, and projects derived from vehicle dynamics that aim to enhance vehicle performance in terms of handling, comfort, and adherence, and to examine safety optimization in the emerging contexts of smart, connected, and autonomous driving.This Special Issue focuses on new findings in the following topics:(1) Experimental and modelling activities that aim to investigate interaction phenomena from the macroscale, analyzing vehicle data, to the microscale, accounting for local contact mechanics; (2) Control strategies focused on vehicle performance enhancement, in terms of handling/grip, comfort and safety for passengers, motorsports, and future mobility scenarios; (3) Innovative technologies to improve the safety and performance of the vehicle and its subsystems; (4) Identification of vehicle and tire/wheel model parameters and status with innovative methodologies and algorithms; (5) Implementation of real-time software, logics, and models in onboard architectures and driving simulators; (6) Studies and analyses oriented toward the correlation among the factors affecting vehicle performance and safety; (7) Application use cases in road and off-road vehicles, e-bikes, motorcycles, buses, trucks, etc.

Technology: general issues --- History of engineering & technology --- tire model parameters identification --- artificial neural networks --- curve fitting --- Pacejka's magic formula --- intelligent vehicles --- autonomous vehicles --- microscopic traffic simulation --- autonomous driving --- friction estimate --- tire-based control --- ADAS --- potential friction --- energy consumption and recovery --- transmission layouts --- fuel-cell electric vehicles --- adhesion enhancement --- dimple model --- patterned surfaces --- viscoelasticity --- enhancement --- articulated vehicles --- stability analysis --- nonlinear dynamic model --- snake instability --- eigenvalue analysis --- central control --- non-linear model-based predictive control --- pitch behavior --- predictive control --- roll behavior --- self-steering behavior --- vehicle dynamics --- viscoelastic modulus --- rubber --- friction --- empirical modeling --- autonomous emergency steering --- multi-input multi-output model predictive control --- actuator dynamics --- control allocation --- handling enhancement --- road friction --- wear --- tyre --- suspension --- semi-active --- handling --- comfort --- optimisation --- directional stability --- road profile --- road unevenness --- vehicle-road interaction --- vertical vehicle excitation --- tire models --- tire tread --- motorcycle --- rider --- screw axis --- weave --- wobble --- multibody --- gravel pavement --- roughness --- straightedge --- power spectral density --- international roughness index --- vehicle response --- driving comfort --- sky-hook --- in-wheel motor --- semi-active suspension --- quarter-car model --- suspension performance --- suspension test bench --- vehicle stability --- road models --- quarter car models --- limit cycles --- acceleration speed portraits --- speed oscillations --- velocity bifurcations --- noisy limit cycles --- limit flows of trajectories --- Sommerfeld effects --- differential-algebraic systems --- polar coordinates of roads --- covariance equations --- stability in mean --- supercritical speeds --- analytical travel speed amplitudes --- Floquet theory applied to limit cycles --- non-pneumatic tire --- finite element analysis --- steady state analysis --- tire characterization --- footprint --- contact patch --- longitudinal interaction --- tire model parameters identification --- artificial neural networks --- curve fitting --- Pacejka's magic formula --- intelligent vehicles --- autonomous vehicles --- microscopic traffic simulation --- autonomous driving --- friction estimate --- tire-based control --- ADAS --- potential friction --- energy consumption and recovery --- transmission layouts --- fuel-cell electric vehicles --- adhesion enhancement --- dimple model --- patterned surfaces --- viscoelasticity --- enhancement --- articulated vehicles --- stability analysis --- nonlinear dynamic model --- snake instability --- eigenvalue analysis --- central control --- non-linear model-based predictive control --- pitch behavior --- predictive control --- roll behavior --- self-steering behavior --- vehicle dynamics --- viscoelastic modulus --- rubber --- friction --- empirical modeling --- autonomous emergency steering --- multi-input multi-output model predictive control --- actuator dynamics --- control allocation --- handling enhancement --- road friction --- wear --- tyre --- suspension --- semi-active --- handling --- comfort --- optimisation --- directional stability --- road profile --- road unevenness --- vehicle-road interaction --- vertical vehicle excitation --- tire models --- tire tread --- motorcycle --- rider --- screw axis --- weave --- wobble --- multibody --- gravel pavement --- roughness --- straightedge --- power spectral density --- international roughness index --- vehicle response --- driving comfort --- sky-hook --- in-wheel motor --- semi-active suspension --- quarter-car model --- suspension performance --- suspension test bench --- vehicle stability --- road models --- quarter car models --- limit cycles --- acceleration speed portraits --- speed oscillations --- velocity bifurcations --- noisy limit cycles --- limit flows of trajectories --- Sommerfeld effects --- differential-algebraic systems --- polar coordinates of roads --- covariance equations --- stability in mean --- supercritical speeds --- analytical travel speed amplitudes --- Floquet theory applied to limit cycles --- non-pneumatic tire --- finite element analysis --- steady state analysis --- tire characterization --- footprint --- contact patch --- longitudinal interaction