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This comprehensive book provides the first unified framework for stability and dissipativity analysis and control design for nonnegative and compartmental dynamical systems, which play a key role in a wide range of fields, including engineering, thermal sciences, biology, ecology, economics, genetics, chemistry, medicine, and sociology. Using the highest standards of exposition and rigor, the authors explain these systems and advance the state of the art in their analysis and active control design. Nonnegative and Compartmental Dynamical Systems presents the most complete treatment available of system solution properties, Lyapunov stability analysis, dissipativity theory, and optimal and adaptive control for these systems, addressing continuous-time, discrete-time, and hybrid nonnegative system theory. This book is an indispensable resource for applied mathematicians, dynamical systems theorists, control theorists, and engineers, as well as for researchers and graduate students who want to understand the behavior of nonnegative and compartmental dynamical systems that arise in areas such as biomedicine, demographics, epidemiology, pharmacology, telecommunications, transportation, thermodynamics, networks, heat transfer, and power systems.

Differentiable dynamical systems --- Differentiable dynamical systems. --- Differential dynamical systems. --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Global analysis (Mathematics) --- Analysis, Global (Mathematics) --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Differential equations --- Topological dynamics

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The study of non-linear dynamical systems nowadays is an intricate mixture of analysis, geometry, algebra and measure theory and this book takes all aspects into account. Presenting the contents of its authors' graduate courses in non-linear dynamical systems, this volume aims at researchers who wish to be acquainted with the more theoretical and fundamental subjects in non-linear dynamics and is designed to link the popular literature with research papers and monographs. All of the subjects covered in this book are extensively dealt with and presented in a pedagogic

Differential geometry. Global analysis --- Differentiable dynamical systems. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics

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The theory of dynamical systems is a major mathematical discipline closely intertwined with all main areas of mathematics. It has greatly stimulated research in many sciences and given rise to the vast new area variously called applied dynamics, nonlinear science, or chaos theory. This introduction for senior undergraduate and beginning graduate students of mathematics, physics, and engineering combines mathematical rigor with copious examples of important applications. It covers the central topological and probabilistic notions in dynamics ranging from Newtonian mechanics to coding theory. Readers need not be familiar with manifolds or measure theory; the only prerequisite is a basic undergraduate analysis course. The authors begin by describing the wide array of scientific and mathematical questions that dynamics can address. They then use a progression of examples to present the concepts and tools for describing asymptotic behavior in dynamical systems, gradually increasing the level of complexity. The final chapters introduce modern developments and applications of dynamics. Subjects include contractions, logistic maps, equidistribution, symbolic dynamics, mechanics, hyperbolic dynamics, strange attractors, twist maps, and KAM-theory.

Differential geometry. Global analysis --- Differentiable dynamical systems. --- Dynamique différentiable --- 531.3 --- Dynamics. Kinetics --- 531.3 Dynamics. Kinetics --- Dynamique différentiable --- Differentiable dynamical systems --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics

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Differential geometry. Global analysis --- Differentiable dynamical systems --- Differentieerbare dynamicasystemen --- Systèmes dynamiques différentiables --- Differential equations, Nonlinear --- Differentiable dynamical systems. --- Numerical Solutions. --- 51 --- -Nonlinear differential equations --- Nonlinear theories --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Mathematics --- Numerical solutions --- -Mathematics --- 51 Mathematics --- -Differential dynamical systems --- Nonlinear differential equations --- Numerical analysis --- Numerical Solutions --- Differential equations [Nonlinear ] --- Differential equations, Nonlinear - Numerical Solutions.

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Differential geometry. Global analysis --- Differentiable dynamical systems --- Point mappings (Mathematics) --- Dynamique différentiable --- 515.16 --- Equations, Recurrent --- Mappings, Point (Mathematics) --- Recurrence relations in functional differential equations --- Recurrent equations --- Functional differential equations --- Mappings (Mathematics) --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Topology of manifolds --- Differentiable dynamical systems. --- Point mappings (Mathematics). --- 515.16 Topology of manifolds --- Dynamique différentiable