How is a fly-by-wire system realized in big planes?
In fact, ARINC 429 is used in the "federated" avionics, this is the "old" system used in many aircraft like A320, B737, ...


Federated avionics require a lot of wires which generates a lot of weight. In ARINC we have approximately one wire per device, so the speed (100Kbps or 12,5Kbps depending on the selected mode) is sufficient.

ARINC 429 Architecture :

In "new" aircraft like A350 or B787 the industry use the Integrated Modular Avionics in order to reduce weight and reduce the number of S/N to stock.


In this kind on avionic all computers are merged in a couple of "cabinet" composed of multiple core processor units, shared ROM, shared RAM, shared graphic cards.
All these cards are linked, in the cabinet, with the Backplane BUS (ARINC 659), which operates at 60Mbps as a commercial aviation bus
All cabinet are linked ,each other and with actuators, using AFDX (ARINC 664) who look like Ethernet protocol and work at the speed of 100Mbit/s.

There is a lot of different IMA architecture with the same principle, but some differences. This is one on them, in this picture you can replace PCI Ex. by ARINC 659 :




Regarding CAN bus, Airbus use in in this A380 (http://www.aviationtoday.com/av/issue/feature/can-bus-in-aviation_31468.html)

Sources : 

http://www.interfacebus.com/Design_Connector_Avionics.html

http://www.modern-avionics.com/

https://en.wikipedia.org/wiki/Avionics_Full-Duplex_Switched_Ethernet