Nonlinear science is ideal for investigating complex problems that arise in biophysical chemistry. Here, we review the approach used in nonlinear science and illustrate the techniques for several problems studied in our group: the peroxidase-oxidase reaction, the influence of nonuniform fields on membrane transport, and finally, neuronal systems and calcium signaling. The mathematical tools that have been derived in the process of studying these systems are also reviewed. Finally, our contributions to some fundamental issues in nonlinear science involving the evolution of chaotic behavior via a torus attractor are reviewed.