Energy harvesters based on non-linear systems are promising devices for extracting energy from mechanical vibrations. This paper presents a new design of energy harvester consisting of two coupled nonlinear systems; the Duffing oscillator and a system with quasizero stiffness. A numerical analysis of the dynamics of the harvester is carried out, presenting coexisting solutions and their energy efficiencies in both chaotic and periodic motion zones. The root mean squared (RMS) voltage results depend on the dimensionless excitation frequency, where high-energy orbits are coexisting with low-energy orbits. In the figures the different impulse characteristics and their sequences for periodic and chaotic zones are presented. Therefore, a detailed analysis is presented for many strategies using an impulse excitation diagram (IED) as a numerical tool for accurately estimating the amplitude of the impulse, its duration, and the moment of initiation. The probability of achieving a given solution is also determined. The simulation results show that achieving the most effective orbit with a single impulse, as well as several impulses, requires similar energy. This results can be a valuable help for designing various systems and strategies for changing the orbit of a solution. Series information Figures and dataseries.Series: The results of numerical calculations: the influence of equivalent stiffness cZ represents the scaling parameter through which the depth of the potential barrier well was mapped. Fig_2a_cz_36_g_5.txt Fig_2a_cz_144_g_174.txt Fig_2a_cz_288_g_1.txt The results of numerical calculations: the influence of geometric quantity a0. Γ represents the scaling parameter through which the depth of the potential barrier well was mapped. Fig2b_a0_003_g_175.txt Fig2b_a0_006_g_5.txt Fig2b_a0_0015_g_1.txt Series of the effective voltage induced on piezoelectric electrodes, which were identified for the shallow and transient well depths of the potential barrier Γ, characterizing the Duffing oscillator to different values of cz and Γ: Fig_6a_cz_144_g_1_p_01.txt Fig_6a_cz_144_g_1_p_02.txt Fig_6a_cz_144_g_1_p_015.txt Fig_6b_p_01_cz_144_g_1.txt Fig_6b_p_01_cz_144_g_5.txt Fig_6b_p_01_cz_144_g_175.txt