The datasets contain the results of numerical simulations of a nonlinear bistable energy harvesting system from ambient vibrating mechanical sources. Detailed model tests of the inertial energy harvesting system consisting of a piezoelectric beam with additional springs were performed. The mathematical model was derived using the bond graph approach. Depending on the choice of spring, the shape of the bistable potential wells was modified, including the removal of the well degeneracy. Consequently, the broken mirror symmetry between the potential wells led to additional solutions with corresponding voltage responses. The probability of occurrence of different high voltage/large orbit solutions with changes in the potential symmetry was investigated. In particular, the periodicity of different solutions with respect to the harmonic excitation period was investigated and compared with respect to the output voltage. The results showed that the subharmonic solution with large orbital period-6 could be stabilized, while some higher subharmonic solutions disappeared with increasing the potential well asymmetry. Changes in the frequency ranges for chaotic solutions were also observed. TXT Files: Fig5a_sigma0.txt - The RMS values of voltage induced on piezoelectric electrodes for p = 0.183 and randomly selected initial conditions: δ = 0, k = 0.5. Fig5b_sigma015.txt - The RMS values of voltage induced on piezoelectric electrodes for p = 0.183 and randomly selected initial conditions: δ = 0.15, k = 0.5. Fig5c_sigma03.txt - The RMS values of voltage induced on piezoelectric electrodes for p = 0.183 and randomly selected initial conditions: δ = 0.3, k = 0.5. Fig5d_sigma06.txt - The RMS values of voltage induced on piezoelectric electrodes for p = 0.183 and randomly selected initial conditions: δ = 0.6, k = 0.5. Fig6a_sigma0_p0183_w19_b.txt - Orbital courses of coexisting periodic solutions, along with probability diagrams illustrating the probability of achieving them ω = 1.9, solutions with a periodicity of 3T. Fig6b_sigma0_p0183_w21_b.txt - Orbital courses of coexisting periodic solutions, along with probability diagrams illustrating the probability of achieving them ω = 2.1, solutions with a periodicity of 9T. Fig6b_sigma0_p0183_w21_g.txt - Orbital courses of coexisting periodic solutions, along with probability diagrams illustrating the probability of achieving them ω = 2.1, solutions with a periodicity of 3T. Fig6b_sigma0_p0183_w21_r.txt - - Orbital courses of coexisting periodic solutions, along with probability diagrams illustrating the probability of achieving them ω = 2.1, solutions with a periodicity of 2T. Fig6c_sigma0_p0183_w26_b.txt - Orbital courses of coexisting periodic solutions, along with probability diagrams illustrating the probability of achieving them ω = 2.6. Solutions with a periodicity of 3T. Fig6c_sigma0_p0183_w26_g.txt - Orbital courses of coexisting periodic solutions, along with probability diagrams illustrating the probability of achieving them ω = 2.6. Solutions with a periodicity of 6T. Fig6c_sigma0_p0183_w26_r.txt - Orbital courses of coexisting periodic solutions, along with probability diagrams illustrating the probability of achieving them ω = 2.6. Solutions with a periodicity of 2T. Fig6d_sigma0_p0183_w38_b.txt - Orbital courses of coexisting periodic solutions, along with probability diagrams illustrating the probability of achieving them ω = 3.8. Solutions with a periodicity of 4T. Fig6d_sigma0_p0183_w38_c.txt - Orbital courses of coexisting periodic solutions, along with probability diagrams illustrating the probability of achieving them ω = 3.8. Solutions with a periodicity of 9T. Fig6d_sigma0_p0183_w38_g.txt - Orbital courses of coexisting periodic solutions, along with probability diagrams illustrating the probability of achieving them ω = 3.8. Solutions with a periodicity of 5T. Fig6d_sigma0_p0183_w38_lb.txt - Orbital courses of coexisting periodic solutions, along with probability diagrams illustrating the probability of achieving them ω = 3.8. Solutions with a periodicity of 7T. Fig6d_sigma0_p0183_w38_r.txt - Orbital courses of coexisting periodic solutions, along with probability diagrams illustrating the probability of achieving them ω = 3.8. Solutions with a periodicity of 3T. Fig7_sigma0_p0183_w21.txt - Numerical results showing the influence of potential asymmetry on the probability of currence of particular solutions for δ = 0.0. Fig7_sigma03_p0183_w21.txt - Numerical results showing the influence of potential asymmetry on the probability of currence of particular solutions for δ = 0.15. Fig7_sigma06_p0183_w21.txt - Numerical results showing the influence of potential asymmetry on the probability of currence of particular solutions for δ = 0.30. Fig7_sigma015_p0183_w21.txt - Numerical results showing the influence of potential asymmetry on the probability of currence of particular solutions for δ = 0.60.