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The aim of the work is to develop and test simple mathematical models suitable for fast and realistic simulations of bifurcation dynamics of systems with a double potential well generated by a pair of repulsive magnets positioned transversely to the direction of motion, where there are motion resistances typical for rolling guides found in industry. Mathematical modelling of a harmonically forced one-degree-of-freedom oscillator with magnetically modified elasticity generating a double symmetrical minimum of potential was carried out. The system is composed of a cart moving along a linear rolling bearing with inertial excitation by means of a stepper motor with an unbalanced disc. The stiffness is realized by a pair of neodymium magnets of axes perpendicular to the direction of motion, in a position corresponding to the static equilibrium position of the oscillator, with additional mechanical linear springs, which generate …