Classification of a stream cipher How would one classify a stream cipher that is neither synchronous, nor self synchronizing?  I would have thought asynchronous, but from all the sources I can find, asynchronous is synonymous with self synchronizing.

The internal state of the cipher is initialized by a key and initialization vector.  The internal state is modified depending on the current internal state, and the previous byte of plain text.  The cipher does not synchronize after a fixed number of bytes.  Error propagation is unlimited, so corruption of one byte of cipher text makes the rest of the message undecipherable.

I would like to know the correct classification of the cipher.

Thanks to @otis and @kodlu, who suggested the terms synchronous and additive.  Searching those terms has led me to this article, describing nearly exactly what I am after.  On page 244, I paraphrase, where W [...] is the running key sequence and where we allow W, to depend both on the secret key (as is customary) and on [all prior bytes of] the plaintext.  This article is heavy on the maths and terms, so many of which I need to look up to understand their meaning.  I am still working through the terms used in the article, which is why I have not proposed an answer to my own question.  I am posting this source, because it might be helpful to someone with a stronger background to answer the question.
Logically I think that should also be a synchronous stream cipher. The word refers to the fact that the keystreams must be synchronized between the encrypter and the decrypter to allow decoding. With anything other than a self-synchronizing cipher that is the case.

However, that does not mesh with existing usage. You will find many texts (example) saying that with synchronous stream ciphers the keystream is independent of the plaintext and ciphertext. So you should definitely not use that term.

Asynchronous is not very good either, for the reason you mention, but you will find it used to describe such ciphers (e.g. Helix here, pdf). So that is probably more understandable than calling them synchronous, even if it too can be confusing. 

If you need to write about it, I would avoid the issue and just call it a stream cipher with a plaintext-dependent keystream. You can say that it is not self-synchronous if you need to make that distinction.