Are there any regulations for the copyright of aircraft's model design between competitors in the aircraft industries? Basically is there a regulation for avoid that one company just steals the project of a competitor to produce a version very close to the original?
This is more of a law issue rather than aviation issue. Anyway here it goes: No, there is no copyright to prevent one manufacturer from copying another aircraft because aircraft design is not protected by copyright.
The first rule about copyright is that it "protects an expression of an idea but not the idea itself". It protects technical diagrams, documents, recording etc, but not the idea expressed in them. Therefore if one simply photocopy the schematics, it would be a copyright violation. But if you reproduce what you see, it is legal.
The word you are probably looking for is "patent", which protects an idea. Aircraft manufacturers do have patents when they come up with something revolutionary. A quick search for "Airbus patent" turns up quite a few results. Whether you agree that particular idea was revolutionary enough for a patent though is another story.
Within countries, you have patents that protect the work of one company from being taken by another. Between companies in different countries is a whole different mess to deal with as some of it depends on diplomatic relations.