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We investigate the chaotic behaviour of multiparticle systems, in particularDNA and graphene models, by applying methods of nonlinear dynamics. Usingsymplectic integration techniques, we present an extensive analysis of chaos inthe Peyrard-Bishop-Dauxois (PBD) model of DNA. The chaoticity is quantified bythe maximum Lyapunov exponent (mLE) across a spectrum of temperatures, and theeffect of base pair (BP) disorder on the dynamics is studied. In addition toheterogeneity due to the ratio of adenine-thymine (AT) and guanine-cytosine(GC) BPs, the distribution of BPs in the sequence is analysed by introducingthe alternation index $\alpha$. An exact probability distribution for BParrangements and $\alpha$ is derived using P\'olya counting. The value of themLE depends on the composition and arrangement of BPs in the strand, with adependence on temperature. We probe regions of strong chaoticity using thedeviation vector distribution, studying links between strongly nonlinearbehaviour and the formation of bubbles. Randomly generated sequences andbiological promoters are both studied. Further, properties of bubbles areanalysed through molecular dynamics simulations. The distributions of bubblelifetimes and lengths are obtained, fitted with analytical expressions, and aphysically justified threshold for considering a BP to be open is successfullyimplemented. In addition to DNA, we present analysis of the dynamical stabilityof a planar model of graphene, studying the mLE in bulk graphene as well as ingraphene nanoribbons (GNRs). The stability of the material manifests in a verysmall mLE, with chaos being a slow process in graphene. For both armchair andzigzag edge GNRs, the mLE decreases with increasing width, asymptoticallyreaching the bulk behaviour. This dependence of the mLE on both energy densityand ribbon width is fitted accurately with empirical expressions.

Chaotic Dynamics of Polyatomic Systems with an Emphasis on DNA Models