Analysis of the dynamics of new models of nonlinear systems with state variable damping and elastic coefficients

Abstract

This paper, is an analysis of the dynamics of new models of nonlinear systems in which the state damping variables with elastic coefficients, given by functions ccos⁡(px), csin⁡(px), ccos⁡(px˙) and csin⁡(px˙) are investigated in their autonomous and excited states. They exhibit periodic regions of stability and instability in their autonomous states and a rich dynamic behavior. The analysis of limit cycles shows the presence of isolated curves around the origin (0.0), which explains the presence of periodic solutions (limit cycles). The dynamics obtained allows to describe qualitatively the cardiac activity (artificial pacemaker). A chaos analysis shows the appearance of regular and chaotic behaviors. These studies allowed us to show the effect of the damping of the state variable and the elastic coefficients on the dynamics of these models. The presence of analog functions makes the experimental study complex. An implementation based on microcontroller simulation technology has been proposed. The microcontroller results are consistent with the numerical results.

Keywords

• Keywords nonlinear systems
• Elastic coefficients
• Limit cycle
• Artificial pacemaker
• State variable damping
• Regular and chaotic behaviors