Chaotic Vibrations of the One-dimensional Wave Equation Due to a Self-excitation Boundary Condition. Iii. Natural Hysteresis Memory Effects
نویسندگان
چکیده
The nonlinear reflection curve due to a van der Pol type boundary condition at the right end becomes a multivalued relation when one of the parameters (α) exceeds the characteristic impedance value (α = 1). From stability and continuity considerations, we prescribe kinematic admissibility and define hysteresis iterations with memory effects, whose dynamical behavior is herein investigated. Assume first that the left end boundary condition is fixed. We show that asymptotically there are two types of stable periodic solutions:
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Chaotic Vibrations of the One-dimensional Wave Equation Due to a Self-excitation Boundary Condition. Ii. Energy Injection, Period Doubling and Homoclinic Orbits
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