There are two approaches, generally speaking.
In the first approach, when you instantiate your next view controller, you could set an array property to "inherit" from the current (soon-to-be previous or parent) view controller:
MyNextViewController *_myNextViewController = [[MyNextViewController alloc] initWithNibName:@"MyNextViewController" bundle:nil];
_myNextViewController.myViewControllerArray = self.myViewControllerArray;
...
In the second approach, you could create a myAppDelegateArray property in your application delegate, instantiating the array when the application initializes (or instantiated somewhere else, on demand).
You can then call the getter for this property from any class — including view controllers.
For example, within an instance of MyNextViewController, you might have a property called myViewControllerArray and you would set it as follows:
self.myViewControllerArray = [UIAppDelegate myAppDelegateArray];
You would add a #define statement somewhere in your application constants file, e.g.:
#define UIAppDelegate ((MyAppDelegate *)[UIApplication sharedApplication].delegate)
or use the full [UIApplication sharedApplication].delegate call, if you prefer.
As a general approach, people seem to prefer the app delegate approach, as it decentralizes access to the desired property.
With this approach, if you rearrange your view controllers or insert new view controllers into your VC hierarchy, you wouldn't need to debug child view controller properties inherited from parent view controllers, because a reference is always available from the app delegate.