How do we keep competitors from simply copying our app?

Protectable IP assets of your app may include the functionality accomplished by the app (potentially protectable under patent), the artwork, code, and U/X you use (protectable in varying degrees under copyright), and the use of the app's name and associated logos (protectable under trademark law).

Preventing others from pragmatically "replicating [y]our software" will require obtaining patent protection, but whether you may do so is a very open question. In the absence of patent protection, your market advantage will need to come by brand awareness and simply having a superior product, customer service, etc.

To determine whether some part of your app may be patent protectable and how best to brand the venture, you should contact a patent/trademark attorney in private.

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This communication: (i) is not a substitute for professional legal advice; (ii) does not create any attorney-client relationship; and (iii) is not a solicitation to offer legal advice. There is no duty to keep any confidential information you disclose in this forum confidential or refrain from providing representation adverse to your interests. You should seek the advice of a licensed attorney in an appropriate jurisdiction before taking any action that may affect your rights.

You need to be very careful here. In the US, you have a 12-month period where you can have something on the market and then file for the patent (this is under the new revisions to the law under the America Invents Act (AIA)). However, this could prevent your ever getting a patent anywhere outside of the US.

At the very least, you should file a provisional before having a public disclosure. That gives you 12 months before you have to file a utility and presumably by then, if you're trying to conserve cash, you'll have a better idea where you stand.

Replicating the functions of software is different then replicating your IP. There are a lot of ways to bake a cookie but if you have a unique process for doing so that's patented, then I simply can't bake them your way, just any other way.

You also don't need to patent everything. You need to look at the most novel aspect of your invention. That may involve the way you move data -- or the nature of the buffering between the app and the entertainment opportunities, etc. You don't need to, nor can you, patent the app itself. Rather you can patent unique methods and any apparatus used therein.

Unfortunately, there is no legal way to prevent others from copying your code or replicating the functions of your app. However, if you have a patent covering your app, then you will have the right to seek an injunction, licensing, or damages from those who infringe on your patent. While software patents have come under much more scrutiny with recent case law, there are still software patents being issued. It may be best to start with a patent feasibility study to see if the novel aspects of your app are patentable given the prior art and current law.