  We investigate the chaotic behaviour of multiparticle systems, in particular
DNA and graphene models, by applying methods of nonlinear dynamics. Using
symplectic integration techniques, we present an extensive analysis of chaos in
the Peyrard-Bishop-Dauxois (PBD) model of DNA. The chaoticity is quantified by
the maximum Lyapunov exponent (mLE) across a spectrum of temperatures, and the
effect of base pair (BP) disorder on the dynamics is studied. In addition to
heterogeneity due to the ratio of adenine-thymine (AT) and guanine-cytosine
(GC) BPs, the distribution of BPs in the sequence is analysed by introducing
the alternation index $\alpha$. An exact probability distribution for BP
arrangements and $\alpha$ is derived using P\'olya counting. The value of the
mLE depends on the composition and arrangement of BPs in the strand, with a
dependence on temperature. We probe regions of strong chaoticity using the
deviation vector distribution, studying links between strongly nonlinear
behaviour and the formation of bubbles. Randomly generated sequences and
biological promoters are both studied. Further, properties of bubbles are
analysed through molecular dynamics simulations. The distributions of bubble
lifetimes and lengths are obtained, fitted with analytical expressions, and a
physically justified threshold for considering a BP to be open is successfully
implemented. In addition to DNA, we present analysis of the dynamical stability
of a planar model of graphene, studying the mLE in bulk graphene as well as in
graphene nanoribbons (GNRs). The stability of the material manifests in a very
small mLE, with chaos being a slow process in graphene. For both armchair and
zigzag edge GNRs, the mLE decreases with increasing width, asymptotically
reaching the bulk behaviour. This dependence of the mLE on both energy density
and ribbon width is fitted accurately with empirical expressions.
