The investigation of chaotic characteristics in multi-well nonlinear systems is one of the key issues for advancing their engineering applications. However, existing studies on the dynamical behaviors of multi-homoclinic orbits and inter-well motions in multistable systems remain insufficient. A spring-coupled rotational inverted pendulum system (SRIP) was established by combining an inverted pendulum and a two-dimensional planar oscillator, enabling the structural multi-stability and homoclinic orbit characteristics to be modulated through parameter adjustments. The equations of motion for both the single-degree-of-freedom(SDOF) and the two-degree-of-freedom(2DOF) SRIP system were derived using Lagrange’s equations. The chaotic response characteristics were then analyzed via the energy and Melnikov functions of homoclinic orbits. The contour plots of energy function for the SDOF SRIP system characterize the topological structures of its phase plane, while the bifurcation characteristics of equilibrium points were examined by analyzing the stability of local extrema in the potential function. Homoclinic bifurcations were depicted by the contours corresponding to the energy levels of unstable equilibrium points. For the 2DOF system, dimensional reduction was performed, and a semi-analytical approach combining Melnikov functions was applied to evaluate the oriented distances between stable and unstable manifolds of various types of homoclinic orbits, thereby characterizing the chaotic responses under perturbations. Numerical simulations validated the analytical results. With increasing coupling stiffness, pitchfork bifurcations of equilibrium points and homoclinic-heteroclinic bifurcations emerge. Under larger excitation amplitudes, both confined and rotational chaos occur, and global characteristics of the attractors were qualitatively analyzed via maximal Lyapunov exponent and Poincar maps.
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