2-D QUADRATIC MAPS AND 3-D ODE SYSTEMS: A RIGOROUS APPROACH by Julien Sprott
This book is based on research on the rigorous proof of chaos and bifurcations in 2-D quadratic maps, especially the invertible case such as the H non map, and in 3-D ODE's, especially piecewise linear systems such as the Chua's circuit. In addition, the book covers some recent works in the field of general 2-D quadratic maps, especially their classification into equivalence classes, and finding regions for chaos, hyperchaos, and non-chaos in the space of bifurcation parameters.Following the main introduction to the rigorous tools used to prove chaos and bifurcations in the two representative systems, is the study of the invertible case of the 2-D quadratic map, where previous works are oriented toward H non mapping. 2-D quadratic maps are then classified into 30 maps with well-known formulas. Two proofs on the regions for chaos, hyperchaos, and non-chaos in the space of the bifurcation parameters are presented using a technique based on the second-derivative test and bounds for Lyapunov exponents. Also included is the proof of chaos in the piecewise linear Chua's system using two methods, the first of which is based on the construction of Poincar map, and the second is based on a computer-assisted proof. Finally, a rigorous analysis is provided on the bifurcational phenomena in the piecewise linear Chua's system using both an analytical 2-D mapping and a 1-D approximated Poincar mapping in addition to other analytical methods.-
CELLULAR NEURAL NETWORKS, MULTI-SCROLL CHAOS AND SYNCHRONIZATION
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ROBUST CHAOS AND ITS APPLICATIONS
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DEVELOPMENT OF MEMRISTOR BASED CIRCUITS
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MATHEMATICAL MECHANICS: FROM PARTICLE TO MUSCLE
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DISCRETE SYSTEMS WITH MEMORY
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BIO-INSPIRED EMERGENT CONTROL OF LOCOMOTION SYSTEMS
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NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE, A (VOLUME II)
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GALLERY OF CHUA ATTRACTORS, A (WITH DVD-ROM)
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EQUATIONS OF PHASE-LOCKED LOOPS: DYNAMICS ON CIRCLE, TORUS AND CYLINDER
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DIFFERENTIAL GEOMETRY APPLIED TO DYNAMICAL SYSTEMS (WITH CD-ROM)
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BIFURCATIONS AND CHAOS IN PIECEWISE-SMOOTH DYNAMICAL SYSTEMS: APPLICATIONS TO POWER CONVERTERS, RELAY AND PULSE-WIDTH MODULATED CONTROL SYSTEMS, AND HUMAN DECISION-MAKING BEHAVIOR
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BIFURCATIONS IN PIECEWISE-SMOOTH CONTINUOUS SYSTEMS
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PHYSARUM MACHINES: COMPUTERS FROM SLIME MOULD
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SYMMETRY AND COMPLEXITY: THE SPIRIT AND BEAUTY OF NONLINEAR SCIENCE
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APPLIED NONLINEAR TIME SERIES ANALYSIS: APPLICATIONS IN PHYSICS, PHYSIOLOGY AND FINANCE
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COUPLED PHASE-LOCKED LOOPS: STABILITY, SYNCHRONIZATION, CHAOS AND COMMUNICATION WITH CHAOS
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MODELING, ANALYSIS AND CONTROL OF DYNAMICAL SYSTEMS WITH FRICTION AND IMPACTS
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CONTINUOUS AND DISCONTINUOUS PIECEWISE-SMOOTH ONE-DIMENSIONAL MAPS: INVARIANT SETS AND BIFURCATION STRUCTURES
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METHODS OF QUALITATIVE THEORY IN NONLINEAR DYNAMICS (PART I)
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CHAOS AND COMPLEXITY IN NONLINEAR ELECTRONIC CIRCUITS
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MODELING LOVE DYNAMICS
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CONTROL OF IMPERFECT NONLINEAR ELECTROMECHANICAL LARGE SCALE SYSTEMS: FROM DYNAMICS TO HARDWARE IMPLEMENTATION
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WAVE MOMENTUM AND QUASI-PARTICLES IN PHYSICAL ACOUSTICS
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UNIVERSALITY AND EMERGENT COMPUTATION IN CELLULAR NEURAL NETWORKS
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DYNAMICAL CHAOS, MODELS AND EXPERIMENTS: APPEARANCE ROUTES AND STRU OF CHAOS IN SIMPLE DYNA SYSTEMS
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HOPF BIFURCATION ANALYSIS: A FREQUENCY DOMAIN APPROACH
| SKU | Unavailable |
| ISBN 13 | 9789814307741 |
| ISBN 10 | 9814307742 |
| Title | 2-D QUADRATIC MAPS AND 3-D ODE SYSTEMS: A RIGOROUS APPROACH |
| Author | Zeraoulia Elhadj |
| Series | World Scientific Series On Nonlinear Science Series A |
| Condition | Unavailable |
| Binding Type | Hardback |
| Publisher | World Scientific Publishing Co Pte Ltd |
| Year published | 2010-07-09 |
| Number of pages | 356 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |