Global dynamics and evolution for the Szekeres system with nonzero cosmological constant term

The Szekeres system with cosmological constant term describes the evolution of kinematic quantities for Einstein field equations in $${\mathbb {R}}^4$$ . In this study, we investigate behavior trajectories presence constant. It has been shown that is a Hamiltonian dynamical system. admits at least two conservation laws, h and $$I_{0}$$ which indicate integrability We solve Hamilton–Jacobi equation, reduce from to an equivalent defined {R}}^2$$ Global dynamics are studied where find there exists attractor finite regime only positive valued $$I_0<-2 .08$$ Otherwise, reach infinity. For $$I_ {0}>0$$ origin also Finally, physical properties by using dimensionless variables different Hubble-normalization conducing {R}}^5$$ see related de Sitter universe