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The rendezvous process is considered a key operation that allows a secondary user (SU) to access an unused authorized spectrum in cognitive radio networks (CRNs). Most existing works focused on fast guaranteed rendezvous without considering a sophisticated jamming attack environment. In this paper, I propose a fast and robust asynchronous rendezvous scheme that can improve robustness against jamming attacks under symmetric asynchronous environments in which all SUs have the same available channels. Unfortunately, in CRNs, each SU can have a different number of available channels due to their relative position to primary nodes (PUs). Therefore, I extend my fast and robust asynchronous rendezvous scheme (FRARS) to a general asymmetric scenario while preserving robustness against jamming attacks. I derive the maximum rendezvous time (MTTR) of my new algorithm and the upper bound of the expected TTR (ETTR) and compare it with the state-of-the-art algorithms such as jump-stay (JS) and Enhanced jump-stay (EJS). My numerical results show that the performance of the proposed technique is better than that of JS and EJS in terms of MTTR and ETTR. Also, the performance will be more significant when there are security concerns about a sophisticated jamming attack.