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Given the more complex dynamical environment, mission applications may also benefit from deeper insight into the attitude motion.
However, we choose to neglect the planet in the remainder of this study as it would lead to more complex dynamical behaviour of the additional, fictitious terrestrial world that is under investigation in this work.
It is shown that a hysteretic system can exhibit more complex dynamical behavior when an external forcing is applied, and that the critical phenomena may exist even when the system reaches its steady state.
Furthermore, there exist more complex dynamical behaviors when h is much bigger as in Figure 11.
In conclusion, the proposed fractional-time SI model can engender more complex dynamical behaviors than its continuous model counterpart.
The time delay of system (1.1) made the system very unstable and led to more complex dynamical behaviors.
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However, observations regarding overall parameter robustness of biological circuits may imply that beyond the apparent model complexity there exists, in a mathematical sense, one or several core systems or operational principles driving the system dynamics that are shielded by the more complex original dynamical equations [ 3- 6].
The key to our approach is to view the identification of multiple ARX models as the identification of a single, though more complex, lifted dynamical model built by applying a polynomial embedding to the input/output data.
When we consider a more complex and realistic dynamical system – the four-body Sun Earth Moon-particle (probe) problem – the trajectorieSun Earth Moon-particlein of inclination when they proberate in the lunar influence sproblemthes allowing trajectoriesn of probes into low-altitude lunar orbits withavegh inclinanions, including polar orbits.
Therefore, we see that the discrete model (2) has more plentiful and complex dynamical behaviors than the continuous model (1).
More complex but related dynamical behaviour has been studied under the names of "chaotic itinerancy" (see for example [260]), "cycling chaos" [131], "networks of Milnor attractors" [261] and "heteroclinic cycles for chaotic oscillators" [262].
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