Front Matter
 Part I Basic Notions and Review
  1 Dynamical Systems and Hyperbolicity
   1.1 Dynamical systems: basic notions
    1.1.1 Systems with continuous and discrete time, and their mutual relation
    1.1.2 Dynamics in terms of phase fluid: Conservative and dissipative systems and attractors
    1.1.3 Rough systems and structural stability
    1.1.4 Lyapunov exponents and their computation
   1.2 Model examples of chaotic attractors
    1.2.1 Chaos in terms of phase fluid and baker’s map
    1.2.2 Smale-Williams solenoid
    1.2.3 DA-attractor
    1.2.4 Plykin type attractors
   1.3 Notion of hyperbolicity
   1.4 Content and conclusions of the hyperbolic theory
    1.4.1 Cone criterion
    1.4.2 Instability
    1.4.3 Transversal Cantor structure and Kaplan-Yorke dimension
    1.4.4 Markov partition and symbolic dynamics
    1.4.5 Enumerating of orbits and topological entropy
    1.4.6 Structural stability
    1.4.7 Invariant measure of Sinai-Ruelle-Bowen
    1.4.8 Shadowing and effect of noise
    1.4.9 Ergodicity and mixing
    1.4.10 Kolmogorov-Sinai entropy
   References
  2 Possible Occurrence of Hyperbolic Attractors
   2.1 The Newhouse-Ruelle-Takens theorem and its relation to the uniformly hyperbolic attractors
   2.2 Lorenz model and its modifications
   2.3 Some maps with uniformly hyperbolic attractors
   2.4 From DA to the Plykin type attractor
   2.5 Hunt’s example: Suspending the Plykin type attractor
   2.6 The triple linkage: A mechanical system with hyperbolic dynamics
   2.7 A possible occurrence of a Plykin type attractor in Hindmarsh-Rose neuron model
   2.8 Blue sky catastrophe and birth of the Smale-Williams attractor
   2.9 Taffy-pulling machine
   References
 Part II Low-Dimensional Models
  3 Kicked Mechanical Models and Differential Equations with Periodic Switch
   3.1 Smale-Williams solenoid in mechanical model: Motion of a particle on a plane under periodic kicks
   3.2 A set of switching differential equations with attractor of Smale-Williams type
   3.3 Explicit dynamical system with attractor of Plykin type
    3.3.1 Plykin type attractor on a sphere
    3.3.2 Plykin type attractor on the plane
   3.4 Plykin-like attractor in smooth non-autonomous system
   References
  4 Non-Autonomous Systems of Coupled Self-Oscillators
   4.1 Van der Pol oscillator
   4.2 Smale-Williams attractor in a non-autonomous system of alternately excited van der Pol oscillators
   4.3 System of alternately excited van der Pol oscillators in terms of slow complex amplitudes
   4.4 Non-resonance excitation transfer
   4.5 Plykin-like attractor in non-autonomous coupled oscillators
    4.5.1 Representation of states on a sphere and equations of the model
    4.5.2 Numerical results for the coupled oscillators
   References
  5 Autonomous Low-dimensional Systems with Uniformly Hyperbolic Attractors in the Poincar´e Maps
   5.1 Autonomous system of two coupled oscillators with self-regulating alternating excitation
   5.2 System constructed on a base of the predator-prey model
   5.3 Example of blue sky catastrophe accompanied by a birth of Smale-Williams attractor
   References
  6 Parametric Generators of Hyperbolic Chaos
   6.1 Parametric excitation of coupled oscillatorsThree-frequency parametric generator and its operation
   6.2 Hyperbolic chaos in parametric oscillator with Q-switch and pump modulation
    6.2.1 Dynamical equations
    6.2.2 Qualitative explanation of the operation
    6.2.3 Numerical results
    6.2.4 Numerical results in the frame of method of slow complex amplitudes
   6.3 Parametric generator of hyperbolic chaos based on four coupled oscillators with pump modulation
    6.3.1 Model, operation principle and basic equations
    6.3.2 Chaotic dynamics: results of computer simulation
   References
  7 Recognizing the Hyperbolicity: Cone Criterion and Other Approaches
   7.1 Verification of transversality for manifolds
    7.1.1 Visualization of the manifolds
    7.1.2 Distributions of angles of the manifold intersections
   7.2 Visualization of invariant measures
   7.3 Cone criterion and examples of its application
    7.3.1 Procedure of verification of the cone criterion
    7.3.2 Examples of application of the cone criterion
   References
 Part III Higher-Dimensional Systems and Phenomena
  8 Systems of Four Alternately Excited Non-autonomous Oscillators
   8.1 Arnold’s cat map dynamics in a system of coupled non-autonomous van der Pol oscillators
   8.2 Dynamics corresponding to hyperchaotic maps
    8.2.1 System implementing toral hyperchaotic map
    8.2.2 Model with cascade transfer of excitation upward the frequency spectrum
   8.3 Hyperchaos and synchronous chaos in a system of coupled non-autonomous oscillators
    8.3.1 Equations and basic modes of operation
    8.3.2 Equations for slow complex amplitudes
   References
  9 Autonomous Systems Based on Dynamics Close to Heteroclinic Cycle
   9.1 Heteroclinic connection: an example of Guckenheimer and Holmes
   9.2 Attractor of Smale-Williams type in a system of three coupled self-oscillators
   9.3 Attractor with dynamics governed by the Arnold cat map
   9.4 Model with hyperchaos
   9.5 An autonomous system with attractor of Smale-Williams type with resonance transfer of excitation in a ring array of van der Pol oscillators
   References
  10 Systems with Time-delay Feedback
   10.1 Some notions concerning differential equations with deviating argument
   10.2 Van der Pol oscillator with delayed feedback, parameter modulation and auxiliary signal
    10.2.1 Attractor of Smale-Williams type in the time-delayed system
    10.2.2 Hyperchaotic attractors
   10.3 Van der Pol oscillator with two delayed feedback loops and parameter modulation
   10.4 Autonomous time-delay system
   References
  11 Chaos in Co-operative Dynamics of Alternately Synchronized Ensembles of Globally Coupled Self-oscillators
   11.1 Kuramoto transition in ensemble of globally coupled oscillators
   11.2 Model of two alternately synchronized ensembles of oscillators
    11.2.1 Collective chaos in ensemble of van der Pol oscillators
    11.2.2 Slow-amplitude approach
    11.2.3 Description of the dynamics in terms of ensembles of phase oscillators
   References
 Part IV Experimental Studies
  12 Electronic Device with Attractor of Smale-Williams Type
   12.1 Scheme of the device and the principle of operation
   12.2 Experimental observation of the Smale-Williams attractor
   References
  13 Delay-time Electronic Devices Generating Trains of Oscillations with Phases Governed by Chaotic Maps
   13.1 Van der Pol oscillator with delayed feedback, parameter modulation and auxiliary signal
   13.2 Van der Pol oscillator with two delayed feedback loops and parameter modulation
   References
  14 Conclusion
   References
 Appendix A Computation of Lyapunov Exponents:The Benettin Algorithm
  References
 Appendix B H´enon and Ikeda Maps
  References
 Appendix C Smale’s Horseshoe and Homoclinic Tangle
  References
 Appendix D Fractal Dimensions and Kaplan-Yorke Formula
  References
 Appendix E Hunt’s Model: Formal Definition
  References
 Appendix F Geodesics on a Compact Surface of Negative Curvature
  References
 AppendixG Effect of Noise in a System with a Hyperbolic Attractor
  References
 Index