Two distinct Josephson junctions (JJs) connected with a constant coupling resistance R(cp) are theoretically considered to investigate the overall dynamics below and above the critical current I(c). The circuit model of the device is driven by two DC current sources, I(1) and I(2). Each junction is characterized by a nonlinear resistive-capacitive junction (NRCSJ). Having constructed the circuit model, time-dependent simulations are carried out for a variety of control parameter sets. Common techniques such as bifurcation diagrams, two-dimensional attractors and Lyapunov exponents are applied for the determination of chaotic as well as periodic dynamics of the superconducting junction devices. According to the findings, two states (namely superconducting and ordinary conducting) are determined as functions of the source currents. The chaotic current which flows through Rcp exhibits a very rich behavior depending on the source currents I(1) and I(2) and junction capacitances C(1) and C(2). The device characteristics are summarized by a number of three-dimensional phase diagrams in the parameter space. In addition, for certain parameters, hyper-chaotic cases with two positive Lyapunov exponents are encountered. In contrast to earlier studies claiming the need for a sinusoidal feeding current for generating a chaotic signal, our circuitry can easily generate one via a DC source. (C) 2009 Elsevier B.V. All rights reserved.