Theoretical analysis and microcontroller implementation of linear resistor-capacitor shunted Josephson junction (LRCSJJ) model are studied in this paper. The rate-equations describing the LRCSJJ model has no or two equilibrium points. One of the equilibrium points is a saddle node and the other one is a stable node. The hysteresis loop of current-voltage curves increases with the rising of the capacitance of Josephson junction (JJ). Excitable mode, limit cycle, periodic and chaotic behaviors are found in LRCSJJ model with external alternative current (AC) source thanks to the two modulation parameters largest Lyapunov exponents (LLE) diagram. LRCSJJ model exhibits two different shapes of chaotic attractors by varying the modulation amplitude. Finally, the existence of chaotic behaviors is confirmed by microcontroller results obtained from the microcontroller implementation of LRCSJJ model.