Hello Dave,
Imagine how you would feel if a stranger suddenly decided to move in with you without your consent or blessing. You are right, your cat has had it's nose put out of joint.
It is quite possible that they both will learn to get along together and maybe even become friends. Equally they may not.
A day is certainly not long enough for them to decide how they are going to get along, but as the only dissension so far is verbal, hissing etc, hopefully this will remain the case and soon your cat will start accepting the new one.
A few things I feel you should do.
1) Try to feed the cats from different bowls.
2) Feed the stray in a different room to where you own cat presently eats.
3) Make sure your cat knows that it is still wanted by petting it.
4) If possible, when you go to bed put the stray in a different room from the one your cat sleeps in for a few days. This should avoid the possibility of the hissing becoming more violent.
Over the years I have cared for many cats and every time a new cat has entered the home, the present cat(s) objected for a few days but it did pass and the new addition soon became a regular family member.
There can be no guarantees of course but fingers crossed thing will work out.
Good luck.
John
(Poseidon)
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