AMERICAN OPERA COMPANIES experienced a marked increase in the number of performances, attendance, and revenues for the 1986-87 season, the Central Opera Service reports. Researchers attribute the upswing to prudent management, stepped-up fund raising, increased donations, and extensive marketing efforts. While there was a general return to all-time favorites, such as works by Mozart and Puccini, new American operas were given more performances by small touring companies for educational purposes. A BRONZE STATUE OF DUKE ELLINGTON in New York's Central Park has been commissioned by cabaret singer Bobby Short to honor the jazz composer and bandleader. ``Salute the Duke,'' a fund-raising concert, takes place Oct. 19 at Lincoln Center, with Mr. Short, Jessye Norman, and the Amherst Saxophone Quartet. The planned 20-foot statue will be sculpted by Robert Graham. THE AWARD-WINNING MUSICAL `CATS,' by Andrew Lloyd Webber, celebrates its fifth anniversary tonight at the Winter Garden Theatre in New York. First produced in London, ``Cats'' continues to sell out in Hamburg, Oslo, and Vienna, as well as cities in Japan and Australia.