This paper introduces a three-stable locally active memristor whose internal state equation is composed of sign functions related to internal state and voltage. The memristor has three asymptotically stable equilibrium points and a locally active region. The non-volatility and local activity of the memristor are verified by the POP (power-off plot) and the DC V - I plot, respectively. Furthermore, the proposed memristor has a petal-like continuous DC V - I curve, and thus it also is a new type of 4-lobe Chua corsage memristor. Biasing the memristor at its locally active region and connecting it in series with an inductor, a second-order oscillator is developed in this paper. The required inductance and the oscillation frequency are determined by analyzing the admittance function Y ( iw,V ) of memristor’s small-signal equivalent circuit. Based on Hopf bifurcation theory and the pole-zero diagram of the composite admittance function Y c ( s , Q ) , the dynamics of the resultant oscillator circuit are analyzed in detail. In addition, a third-order chaotic oscillation circuit is obtained by adding a capacitor to the second-order oscillation circuit. Its dynamical characteristics are analyzed through Lyapunov exponent spectrum, bifurcation diagram and dynamic diagram. Finally, simulation results based on Multisim are given to verify the correctness of the numerical simulation.