Anharmonic effects on the dynamic behavior’s of Klein Gordon model’s

Highlights：

• Theoretical nonlinear Klein Gordon model with anharmonic, cubic and quartic interactions between nearest neighbor particles immersed in a parametrized on-site substrate potential is presented.

• Illustration of theoretical model by introducing a discrete nonlinear electrical transmission line.

• The mathematical model which derive is a new class of differential equations possessing several key parameters and ranging from many singular straight lines.

• Dynamical system methods are used to discuss bifurcations of phase portraits and vector fields for each orbit of phase portraits with corresponding conditions.

• All possible exact parametric representations of solutions are compute and phenomena such as the formation of cracks originating from dislocations that are observed in semiconductor heterostructures can now have a beginning of analytical explanations.