Abstract
Consider the family of differential equations on the cylinder, dx/dt = a(t) + b(t) x , where x, t ∈ ℝ, and a, b are real, 1-periodic and smooth functions. The solutions satisfying x(0) = x(1) are called periodic orbits of the equation. The periodic orbits that are isolated in the set of all the periodic orbits are usually called limit cycles. We give a proof, which is self contained, that there is no upper bound for the number of limit cycles of the above type of equations.
Original language | English |
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Pages (from-to) | 29-34 |
Journal | Communications on Applied Nonlinear Analysis |
Volume | 15 |
Issue number | 1 |
Publication status | Published - 1 Jan 2008 |
Keywords
- Bifurcations
- Limit cycles
- Non-smooth differential equations