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We discuss the extraction of few-parameter, global dynamical models from noisy time series of chaotic systems. In particular, we consider the class of models which are approximations to sets of dynamical equations in the reconstructed phase space. We show that certain numerical methods significantly improve the quality of the resulting models, and central to these methods is the idea of eliminating model terms which are “dynamically insignificant” and add only numerical noise. For the purposes of the paper, we quantify model quality by the rather strict measure of its ability to recover the dynamical invariants of the original system, in particular, the Lyapunov spectrum. Consequently, we also postulate that by first extracting a global model, the Lyapunov spectrum of a generating system can be recovered from time series whose noise levels are much higher than current algorithms would allow. We present several numerical examples to demonstrate the above ideas.

The next-generation Airborne Collision Avoidance System (ACAS X) is currently being developed and tested to replace the Traffic Alert and Collision Avoidance System (TCAS) as the next international standard for collision avoidance. To validate the safety of the system, stress testing in simulation is one of several approaches for analyzing near mid-air collisions (NMACs). Understanding how NMACs can occur is important for characterizing risk and informing development of the system. Recently, adaptive stress testing (AST) has been proposed as a way to find the most likely path to a failure event. The simulation-based approach accelerates search by formulating stress testing as a sequential decision process then optimizing it using reinforcement learning. The approach has been successfully applied to stress test a prototype of ACAS X in various simulated aircraft encounters. In some applications, we are not as interested in the system's absolute performance as its performance relative to another system. Such situations arise, for example, during regression testing or when deciding whether a new system should replace an existing system. In our collision avoidance application, we are interested in finding cases where ACAS X fails but TCAS succeeds in resolving a conflict. Existing approaches do not provide an efficient means to perform this type of analysis. This paper extends the AST approach to differential analysis by searching two simulators simultaneously and maximizing the difference between their outcomes. We call this approach differential adaptive stress testing (DAST). We apply DAST to compare a prototype of ACAS X against TCAS and show examples of encounters found by the algorithm.

ABSTRACT. Positive phonotaxis to tape recorded conspecific song by males of the katydid Neoconocephalus affinis (Beauvois) (Orthoptera: Tettigoniidae) was studied in the field, in Puerto Rico. N.affinis males stridulated loudly during evening hours, and most males were territorial. Aggression between neighbours occurred, albeit rarely, and playback experiments using tape recordings of N.affinis song showed that aggressive behaviour, in the form of jumps directed toward a loudspeaker, could be elicited from a male by song broadcast above a threshold sound intensity. Response thresholds for different males varied from 76 to 93 dB, intensities that corresponded to calculated inter‐neighbour distances of 1.6‐0.26 m, respectively. Insects that had lower response thresholds were on average more isolated from neighbours and also stridulated more persistently and at a higher sound intensity than insects with higher response thresholds. N.affinis males displayed no phonotaxis toward the song of Neoconocephalus maxillosus, a sympatric species whose song is similar to that of N.affinis in principal frequency but differs in wingstroke rate. Phonotaxis toward conspecific song could only be elicited from males while they were silent.