ARP ODYSSEi is described as 'masterful recreation of Korg's legendary 1972 synthesizer, the ARP Odyssey. It's a polyphonic, analog synth made exclusively for iOS from the masters themselves'. There are eight alternatives to ARP ODYSSEi for a variety of platforms, including iPad, iPhone, Mac, AudioBus and Windows. The best alternative is Moog Model 15. It's not free, so if you're looking for a free alternative, you could try KORG Gadget. Other great apps like ARP ODYSSEi are DRC - Polyphonic Synthesizer (Paid), Poison-202 (Paid), KORG iWAVESTATION (Paid) and KORG iMS-20 (Paid).
DRC is a virtual analog synthesizer replicating the sound of hardware synths and featuring a minimal but powerful parameter set and cloud syncing for presets to make it easy to port patches to other devices.
Animoog captures the vast sonic vocabulary of Moog synthesizers and applies it to the modern touch surface paradigm, enabling you to quickly sculpt incredibly fluid and dynamic sounds that live, breathe, and evolve as you play them.