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by Albert C. J. Luo
Toward Analytical Chaos in Nonlinear Systems
Cover
Title Page
Copyright
Preface
Chapter 1: Introduction
1.1 Brief History
1.2 Book Layout
Chapter 2: Nonlinear Dynamical Systems
2.1 Continuous Systems
2.2 Equilibriums and Stability
2.3 Bifurcation and Stability Switching
Chapter 3: An Analytical Method for Periodic Flows
3.1 Nonlinear Dynamical Systems
3.2 Nonlinear Vibration Systems
3.3 Time-Delayed Nonlinear Systems
3.4 Time-Delayed, Nonlinear Vibration Systems
Chapter 4: Analytical Periodic to Quasi-Periodic Flows
4.1 Nonlinear Dynamical Systems
4.2 Nonlinear Vibration Systems
4.3 Time-Delayed Nonlinear Systems
4.4 Time-Delayed, Nonlinear Vibration Systems
Chapter 5: Quadratic Nonlinear Oscillators
5.1 Period-1 Motions
5.2 Period-m Motions
5.3 Arbitrary Periodical Forcing
Chapter 6: Time-Delayed Nonlinear Oscillators
6.1 Analytical Solutions
6.2 Analytical Bifurcation Trees
6.3 Illustrations of Periodic Motions
References
Index
End User License Agreement
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References
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End User License Agreement
Index
Analytical bifurcation tree
Analytical solution
Arbratrary periodical forcing
Asymptotically stable equilibrium
Asymptotically unstable equilibrium
Autonomous dynamical systems
Autonomous nonlinear system
Autonomous time-delayed nonlinear system
Bifurcation
Bifurcation of periodic flow
Bifurcation of periodic motion
Bifurcation of period-
m
flow
Bifurcation of period-
m
motion
Bifurcation point
Bifurcation value
Center
Center subspace
Center manifold
Complex eigenvalues
Continuous dynamical system
Circular equilibrium
Critical point
Critical equilibrium
Derative
Degenrate equilibrium
Decresasing saddle
Differentiable manifold
Dynamical system
Eigenspace
Eigenvalue
Equilibrium
Equilibrium point
Flow
Fourier Series Solutions
Free vibration systems
Frequency-amplitude characteristics
Generalized coordinite transformation
for periodic flow
for periodic motion
for period-
m
flow
for period-
m
motion
Homeomorphism
Hopf bifurcation
Hyperbolic equilibrium
Hyperbolic points
Hyperbolic-spiral stable chaos
Hyperbolic-spiral unstable chaos
Hyperbolic stable chaos
Hyperbolic unstable chaos
Integral
Incresasing saddle
Invariant circle
Invariant subspace
C
r
invariant manifold
Jacobian matrix
Jacobian determinant
Linearized system
Lipschitz condition
Lipschitz constant
Local stable invariant manifold
Local stable manifold
Local unstable invariant manilfod
Local unstable manifold
Manifold
Nonautonomous dynamical systems
Nonautonomous nonlinear systems
Nonautonomous Time-delayed nonlinear systems
Nonlinear vibration systems
Nonlinear dynamical system
Norm
Operator norm
Period-1 motion
Period-doubling Hopf bifurcation
Period-
m
flows
Period-
q
Hopf bifurcation
Period-
p/q
Hopf biufcation
Periodic flow
Pitchfork bifurcation
Period-doubling solutions
Periodically excited vibration system
Periodically excited vibration systems with time-delay
Periodically forced, nonlinear system
Perioidcally forced, time-delayed, nonlinear system
Perioidcally forced, time-delayed, nonlinear system vibration
Quadratic nonlinear oscillator
Quasi-periodic flows
Quasi-period-
p
k
Hopf bifurcation
Saddle
Saddle unstable chaos
Saddle-node bifurcation
Sink
Source
Spiral saddle unstable chaos
Spiral stable chaos
Spiral unstable chaos
Spatial derivative
Spirally stable equilibrium
Spirally unstable equilibrium
Stability switching
Stability of periodic flow
Stability of periodic motion
Stability of period-
m
flow
Stability of period-
m
motion
Stable equilibrium
Stable node
Stable subsapce
Switching
Switching points
Switching values
Time-delayed nonlinear oscillator
Time-delayed, quadratic nonlinear oscillator
Time-delayed nonlinear system
Time-delayed, nonlinear vibration systems
Time-delayed, free vibration systems
Trajectory
Transcritical bifurcation
Unstable equilibrium
Unstable Hopf bifurcation
Unstable node
Unstable saddle-node bifurcation
Unstable subspace
Vector field
Vector function
Velocity vector
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