Kachura and Schneider's theory.

The inner circle represents the traditional bases of English: the United Kingdom, the united states, Australia, New Zealand, Ireland, anglophone Canada, and some Caribbean territories. Total number of English speakers in the inner circle is as high as 380 million, of whom some 120 million are outside the United States.

Next is the outer circle, which includes countries where English is not the native language. However is important for historical reasons and plays a part in national institutions. this circle includes India, Nigeria, the Philippines, Bangladesh, Pakistan, Malaysia, Tanzania, Kenya etc. 
The total number of speakers in the outer circle is estimated a range of 150 million to 300 million. 

Finally, the expanding circle encompasses those countries where English plays no historical or governmental role, but where it is nevertheless widely used a foreign language or lingua franca. This includes much of the worlds population. Much of the world is Norm developing.  ''norm-dependent', because it relies on the standards set by native speakers in the inner circle.

Edgar Schneider - Developmental stages for the new varieties of English. 

The closer the contact (language contact), higher the degree of bilingualism, multilingualism in a community, the stronger the effects of contact. 

1. The structural effects of language contact depend on social conditions. Therefore, history will play an important part. 

2. Contact induced changes can be achieved by a variety of mechanisms, from code switching. Occurs when a speaker alternates between two or more languages, or language varieties, in the context of a single conversation) to code alternation to acquisition strategies. (Language acquisition usually refers to first-language acquisition, which studies infants' acquisition of their native language. This is distinguished from second language acquisition, which deals with the acquisition (in both children and adults) of additional languages). 

3. Language evolution, and the emergence of contact induced varieties, can be regarded as speakers making selections from a pool of linguistic variants made available to them. 

4. Which features will be ultimately adopted depends on the complete 'ecology' of the contact situation, including factors such as demography, social relationships, and surface similarities between languages etc.