In this paper, we report the existence of bursting oscillations in systems governed by a second-order differential equation with only one signum nonlinearity term and time-delay feedback, driven by the slowly varying external force. Depending on the sign of the strength of signum nonlinearity, two cases are studied: two-well and single-well potentials. The external force acts as the control parameter, the stability of equilibrium points is first discussed and the condition for Hopf bifurcation is established. Secondly, we present the effect of time delay on bursting oscillations when periodic forcing changes slowly. Our results show that the time delay is responsible for the appearance or disappearance of the bursting phenomenon. It is also found that the amplitude, the number of peaks and period of bursting oscillation depend on the value of the time delay. The bursting shapes obtained theoretically are exhibited experimentally using the real microcontroller simulation.

在本文中，我们报告了由缓慢变化的外力驱动的仅具有一个符号非线性项和时滞反馈的二阶微分方程控制的系统中的爆裂振动的存在。根据信号非线性强度的符号，研究了两种情况：两势和单势势。外力作为控制参数，首先讨论了平衡点的稳定性，并确定了Hopf分叉的条件。其次，我们介绍了当周期性强迫缓慢变化时，时间延迟对猝发振荡的​​影响。我们的结果表明，时间延迟是导致突发现象出现或消失的原因。还发现振幅 峰值数量和突发振荡的周期取决于时间延迟的值。理论上获得的爆裂形状通过实际的微控制器仿真实验显示出来。