Dont worry, and dont set it up so that he *becomes* stubborn. If he's hungry, he'll eat. If (and I would not worry with a 13mo kid just yet, I do with my 6.5yo kid) he refuses dinner because he is holding out for dessert (ice cream in my son's case) then no, when he is hungry, he gets to eat dinner or something healthyish (ie, apples or bread & jam, but no sweets if he didnt eat his dinner).
I really think it has more to do with his growth rate and appetite cycle. My son (a very skinny little thing!) is absolutely famished when he gets home from school and will eat and eat and eat! (if you know my son, that's something to go wow!!! about!) Then at dinner, he will not eat! So ideally for him, I would have dinner at 4.
And, when he is about to have a growth spurt, you'll see him eating more, eating dinner, etc. Then it will drop off again.
Really, all you need to do is make healthy food choices available (give him a couple choices, because some days I just dont feel like eating oatmeal or green beans but other days I do want that) and when he's hungry, he'll eat.
Another big thing I learned with my son is to "close the kitchen" or stop letting him snack for an hour or two before dinner. Usually he ate breakfast good (like me, about an hour after getting up, we just aren't hungry when we wake up like my husband is), lunch ok, and it tended to go on and on when he was a toddler, so pretty much constant snacking all through the day really. Feed him a good healthy/filling snack like a banana or peanut butter & crackers or something that to us is just a snack but to a kid really is more like a mini meal) at 3ish then NO MORE FOOD until dinnertime at 5 or 6 (adjust to your schedule, ie if dinner is at 7, stop at 5). That was the best way I found to get him to eat more at dinnertime.
Now it's hard for me because at almost 8 he just goes and helps himself from the pantry or fridge when he's still "starving" after a bagel and an apple and a yogurt and I say ENOUGH, wait for dinner! Then of course at dinner he doesnt eat. but bagel+apple+yogurt = ok nutrition, not what I *want* him to be eating but ok enough, it's not chips and sodas and candy and ice cream.
Another tip to getting younguns to eat better is to offer dips. Simple stuff like tube pasta and a little cup of sauce, they can dip and eat. (that's the same as spaghetti) Or chicken cut up into strips/bites and sauce or dressing for them to dip and eat. My son suddenly started eating salad when he asked me for dressing and always (and only) ate it if he had dressing. (silly me. I thought toddlers liked plain lettuce haha)
Make ketchup, ranch dressing, sauce, soft peanut butter, and the like your mealtime friend. I saved some of those plastic cups that came in the pillsbury sweet cinnamon/orange rolls tubes, or the scoops from the big lemonaid drink mix, etc. Those little cups are nice (even a little measuring cup or dixie bathroom cups will be fine!) because otherwise the ketchup/whatever gets spread all over the plate and they need more cuz it's not in a pile anymore!