The members of my species don't have territories, and because of their migratory nature material possessions are not that important to them. The reason for this is because they live on a world where the days last 9 years. I can see crime like murdering someone over food, but would wars and battles occur? Even if they would, why would they fight?
There are many different reasons for starting a war. Here are some:
Resources. Nation-state X has something that nation-state Y needs or wants pretty desperately. Nation-state Y's easiest course in many cases would be to simply reach a trade agreement: We'll give you this much food for this much wood. However, if nation-state X really needs or wants the wood, thought, then they would not be inclined to accept the offer, and the agreement goes nowhere. Nation-state Y then prepares for war.
In your world, there are some interesting important resources. Bowlturner pointed out that lifting gas would be important. This is an excellent example because helium has historically been much more expensive than hydrogen; this is why hydrogen was used for airships in many cases, despite its tendency to explode under certain conditions. Here are some other possibilities for your world:
- Lightweight materials (ever kilogram counts!)
- Non-flammable materials (if hydrogen was used in lieu of helium)
- . . . ?
Religion. Religious wars happen, as we seem to have collectively determined this week. Nation-state X is made up of heathens - according to the religious leaders of nation-state Y - and so we must all go and kill them! For nations with roughly religiously homogenous populations, religious wars become more of a possibility.
I can't come up with anything specific for your world, because there doesn't seem to be anything that would severely influence religious practices as a whole there.
A madman. Franklin Roosevelt was not alone in proclaiming that Adolf Hitler was a madman; whether or not that description is apt is up to you to decide, but the results of a madman gaining total power would be comparably catastrophic.
In your world, this scenario seems to be perfectly possible, although it seems that catastrophes would be easier to unleash. A simultaneous ignition of flammable gases in lifting compartments, or a release of lifting gases, could send a rival city crashing to the ground. Even someone acting alone could do this - a scary thought. Alliances then come into play, even if the original nation-state was entirely destroyed.
Genocide. This is similar to religious wars inasmuch as it involves nation-state Y trying to destroy the people of nation-state X simply because of some certain - possibly entirely superficial and unimportant - characteristic.
These could all happen in any setting, though I've talked about some specific examples unique to your world (see this for some related ideas). Here are some more interesting scenarios that could only happen in the land of floating, migratory cities:
City X happens to have caught a rather nice air current that is helping them move swiftly from point A to point B, and they manage to stop other cities from using it. City Y is annoyed and starts a war.
Someone who claims to be from City X initiates a terrorist attack against City Y by damaging or destroying compartments with lifting gases (as I talked about in the madman section). Whether or not he is actually from City X is immaterial; City Y has justification to attack City X.
City X is hovering over City Y, causing City Y to lose all energy (I believe you said they are solar powered). City Y must fight back for revenge!
They might be smaller but the plains Indians migrated around following the herds and they attacked each other. It might have been for water holes, or prey or raiding for women but they did attack each other.
If this is in your planet with floating cities, then there are more resources to steal: the gas in the zeppelins could be very much worth the price of an attack. and even the balloons themselves could be a valuable commodity.
As long as people think it would be easier to take from someone else, than get or find it themselves, there will be theft and war.
What about food and water? That is a every good reason to wage war. They move from oases to oases (to avoid depleting the resources) or following the monsoon. They might keep animals with them (livestock) but need to give them food. Nomadic people have fought to get the best pastures in order to feed their animals and themselves. So, yes they would fight to keep the best resources for themselves.
The climate is not constant, it's always fluctuating. Some years are drier than other and will put a strain on the resources. This is another source of conflict.
as already stated, war will happen. war is about wanting something the other people have. If anything I think war is more common with migrating species. With territories there is a clear "this is mine, that is yours" divide, defined by where your territory ends, that makes it easy to understand who expects to own what. When migrating you don't know who owns what. If both show up at the same watering hole neither has any more of a claim on it then the other, which means both sides feel more justified in claiming it as theirs (and thus fighting over it) then if one side knows the other has a fair claim of the water being in their pre-owned Territory.
Also, keep in mind if this is your earlier world there likely would be a territory of sorts. Everyone is migrating in the same direction, so territory would likely be divided by the ring you make around the planet. You expect to always be able to migrate along this path. Or actually it would be more like "I own locations X, Y , and Z, and the right to travel to them. I will be in one of those positions depending on what year it is, but I expect that each of those locations is my territory when I migrate to it. Over enough time everyone will get predefined locations they travel to and set up 'home' for 3 years.
Are they migratory, or nomadic? If migratory, like birds, they have (at least) two home regions and travel between them. Getting from one home to another earliest to occupy the best spot would definitely be a source of tension, possibly sabotage to delay the other party would be an option to get ahead. If that's not enough cause for war, wait until your spot's previous owner turns up later...
Or are there regular migration routes, and another, settled, species on the path? Having your neighbourhood torn up twice a year by the nomads would be another cause of strife. The Plains Indians have already been mentioned : I understand farmers who settled on their routes didn't always get on too well with them.
Resources are the most common reason for war, and territory is just what happens to decide upon who gets access to resources.
In your world, people cannot stick around to exploit resources, so they wander all the time. Nevertheless, they need resources - food, water, materials of all kinds. Why would they not fight over them? The main difference between our world and theirs would be that they fight only for temporary access to resources, so there would be more wars, but possibly less destructive ones. The option to simply move to the next resource would always be present, but since access is never permanent, you would fight over the same resource again and again (basically, every time you come to it on your migration).