Two built-in features of WordPress make this easy to accomplish, without any code: body tag classes, and the ability to add a class to a menu item.
Any author archive pages will have the classes ‘archive’ and ‘author’ in the tag (along with others, including author-name and author-id).
You can add a class to a menu item by opening the Screen Options tab on the menu page and clicking the ‘CSS Classes’ checkbox. Add a class name and save the menu.
In your CSS, you can then target that menu item when the body tag has ‘author’ class.
Example:
body.author .menu-item.myclassname { active state rules here }