Shil’nikov chaos in the oxidation of formic acid with bismuth ion on Pt ring electrode

Tunable bimodal explorations of space from memory-driven deterministic dynamics

We present a wave-memory-driven system that exhibits intermittent switching between two propulsion modes in free space. The model is based on a pointlike particle emitting periodically cylindrical standing waves. Submitted to a force related to the local wave-field gradient, the particle is propelled, while the wave field stores positional information on the particle trajectory. For long memory, the linear motion is unstable and we observe erratic switches between two propulsive modes: linear motion and diffusive motion. We show that the bimodal propulsion and the stochastic aspect of the dynamics at long time are generated by a Shil'nikov chaos. The memory of the system controls the fraction of time spent in each phase. The resulting bimodal dynamics shows analogies with intermittent search strategies usually observed in living systems of much higher complexity.

Irregular polarographic currents obey Feigenbaum universality route from order to chaos

The DC polarograms of an oligomer with four repetitive units of ‘extended viologen’ yield in part irregular current fluctuation. The analysis of the current–time transients at different potentials confirms the periodicity, the period doubling and transfer to chaos. The periodicity doubling obeys the universal route to chaos. The estimated value of the Feigenbaum constant 4.68 is very close to the theoretical value δ = 4.6692...