For a Sun-like star with Jupiter-like and Neptune-like planets, dynamics changes sharply at a mutual inclination near 30-40 degrees, where the planets' precession frequencies become equal.
Chaos in multiplanetary extrasolar systems
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abstract
Here we present an initial look at the dynamics and stability of 178 multiplanetary systems which are already confirmed and listed in the NASA Exoplanet Archive. To distinguish between the chaotic and regular nature of a system, the value of the MEGNO indicator for each system was determined. Almost three-quarters of them could be labelled as long-term stable. Only 45 studied systems show chaotic behaviour. We consequently investigated the effects of the number of planets and their parameters on the system stability. A comparison of results obtained using the MEGNO indicator and machine-learning algorithm SPOCK suggests that the SPOCK could be used as an effective tool for reviewing the stability of multiplanetary systems. A similar study was already published by Laskar and Petit in 2017. We compared their analysis based on the AMD criterion with our results. The possible discrepancies are discussed.
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Dynamical regimes of two eccentric and mutually inclined giant planets
For a Sun-like star with Jupiter-like and Neptune-like planets, dynamics changes sharply at a mutual inclination near 30-40 degrees, where the planets' precession frequencies become equal.