The analysis of NSG system for existence of Si'lnikov chaos

To our knowledge the article in hand is first ever study for existence of Si'lnikov type of chaos for Nuclear Spin Generator (NSG) system. This paper deals with the existence of heteroclinic Si'lnikov-type orbits within an NSG chaotic system involving three parameters and having three equilibrium points. Method of undetermined coefficient is applied for analytical analysis of heteroclinic orbits. As an outcome the Si'lnikov criteria guarantees that the NSG system has a Smale horseshoe type chaos. Uniform convergence of series expansion for heteroclinic orbit is verified in this paper. Lyapunov exponents spectrum and sensitivity dependence are discussed. Numerical simulations are compiled for the verification of analytical results and bifurcation diagrams are displayed. Though examination of Si'lnikov criterion for NSG system is an exhaustive study but we have succeeded to explore an other aspect of the system by this criterion.