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We investigate chaotic to integrable transition in two types of hybrid SYKmodels which contain both $ q=4 $ SYK with interaction $ J $ and $ q=2 $ SYKwith an interaction $ K $ in type-I or $(q=2)^2$ SYK with an interaction $\sqrt{K} $ in type-II. These models include hybrid Majorana fermion, complexfermion and bosonic SYK. For the Majorana fermion case, we discuss both $ N $even and $ N $ odd case. We make exact symmetry analysis on the possiblesymmetry class of both types of hybrid SYK in the 10 fold way by Random MatrixTheory (RMT) and also work out the degeneracy of each energy levels. Weintroduce a new universal ratio which is the ratio of the next nearestneighbour (NNN) energy level spacing to characterize the RMT. We perform exactdiagonalization to evaluate both the known NN ratio and the new NNN ratio, thenuse both ratios to study Chaotic to Integrable transitions (CIT) in both typesof hybrid SYK models. Some preliminary results on possible quantum analog ofKolmogorov-Arnold-Moser (KAM) theorem and its dual version in the quantumchaotic side are given. We explore some intrinsic connections between the twocomplementary approaches to quantum chaos: the RMT and the Lyapunov exponent bythe $ 1/N $ expansion in the large $ N $ limit at a suitable temperature range.Comments on some previously related works are given. Some future perspectives,especially the failure of the Zamoloddchikov's c-theorem in 1d CFT RG flow areoutlined.

A new universal ratio in Random Matrix Theory and chaotic to integrable transition in Type-I and Type-II hybrid Sachdev-Ye-Kitaev models