## Elegant Chaos: Algebraically Simple Chaotic FlowsThis heavily illustrated book collects in one source most of the mathematically simple systems of differential equations whose solutions are chaotic. It includes the historically important systems of van der Pol, Duffing, Ueda, Lorenz, Rossler, and many others, but it goes on to show that there are many other systems that are simpler and more elegant. Many of these systems have been only recently discovered and are not widely known. Most cases include plots of the attractor and calculations of the spectra of Lyapunov exponents. Some important cases include graphs showing the route to chaos.The book includes many cases not previously published as well as examples of simple electronic circuits that exhibit chaos. No existing book thus far focuses on mathematically elegant chaotic systems. This book should therefore be of interest to chaos researchers looking for simple systems to use in their studies, to instructors who want examples to teach and motivate students, and to students doing independent study. |

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### Contents

1 Fundamentals | 1 |

2 Periodically Forced Systems | 41 |

3 Autonomous Dissipative Systems | 61 |

4 Autonomous Conservative Systems | 95 |

5 Lowdimensional Systems D 3 | 109 |

6 Highdimensional Systems D 3 | 115 |

7 Circulant Systems | 165 |

8 Spatiotemporal Systems | 195 |

9 TimeDelay Systems | 221 |

10 Chaotic Electrical Circuits | 233 |

265 | |

281 | |

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### Common terms and phrases

artificial neural network attractor as shown autonomous basin of attraction behavior capacitor capacitor voltage chaotic sea chaotic solutions chaotic systems chaotic travel wave Chlouverakis Chua’s circuit circulant system complex oscillators conservative system corresponding damped derivative differential equations dimension diode dissipative system dynamical system elegant energy exhibit chaos flow forced pendulum Hamiltonian hyperchaotic inductor initial conditions x0,y0,z0 initial conditions xi0 jerk systems Kuramoto–Sivashinsky limit cycle linear Lorenz attractor Lorenz system Lyapunov exponent Model Equation negative neon lamp Nmin nonlinear oscillators ODEs operational amplifier orbit oscillators in Eq parameters pendulum in Eq periodically forced piecewise-linear plot as shown Poincaré section Pol oscillators produce chaos quadratic nonlinearities relaxation oscillator ring of coupled Rössler shown in Fig sinx space plot spatial Spatiotemporal plot Sprott strange attractor system from Eq system in Eq term three-dimensional trajectory travel wave PDE typically uxxxx variables velocity wave PDE variant Waveform zero