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This thesis studies the phenomenon and applications of cooperative behaviour exhibited by coupled chaotic systems. This form of cooperative behaviour is known as chaos synchronisation. The systematic study of chaos synchronisation here contributes to the formulation of chaos theory where the theoretical basis spans between applied mathematics and physical sciences. The new findings in coupled chaotic systems reported in this thesis provide important solutions to some of the existing fundamental problems in chaos theory. This led us to novel discoveries that could be useful in many fields of science and technology, with special focus on cryptography and digital communication. The two main findings introduced in this thesis include controlled projective synchronisation and pseudo-random switching key. In controlled projective synchronisation, a newly derived control function allows us to manipulate the scaling feature of the coupled system. In terms of applications, this discovery shifted chaos-based digital communication to a truly M-ary transmission where each digital symbol can now consists of more than one bit which allows faster transmission rate and lower bit error ratio. In another finding, it is observed that identical synchronisation of chaos is still achievable in coupled chaotic system even with the sub-systems having different initial parameters that switch values within a chosen set in a discontinuous, rapid and random-like manner, refers to as pseudo-random switching keys. This observation opposes to the earlier belief that identical synchronisation can only be realised with identical and fixed system parameters. Incorporating pseudo-random switching keys into cryptography leads to the development of two highly secure cryptosystems. I ATTENTION: The Singapore Copyright Act applies to the use of this document. Nanyang Technological University Library

Chaos synchronisation, control and its application in digital communications