Spontaneous symmetry breaking in amnestically induced persistence

Abstract

We investigate a recently proposed non-Markovian random walk model characterized by loss of memories of the recent past and amnestically induced persistence. We report numerical and analytical results showing the complete phase diagram, consisting of 4 phases, for this system: (i) classical nonpersistence, (ii) classical persistence (iii) log-periodic nonpersistence and (iv) log-periodic persistence driven by negative feedback. The first two phases possess continuous scale invariance symmetry, however log-periodicity breaks this symmetry. Instead, log-periodic motion satisfies discrete scale invariance symmetry, with complex rather than real fractal dimensions. We find for log-periodic persistence evidence not only of statistical but also of geometric self-similarity.

4 pages, 2 color figs

References in corpus (4)

• Predictability of catastrophic events: material rupture, earthquakes, turbulence, financial crashes and human birth
• Elephants can always remember: Exact long-range memory effects in a non-Markovian random walk
• Amnestically induced persistence in random walks
• Analytic Formulation, Exact Solutions, and Generalizations of the Elephant and the Alzheimer Random Walks

Cited by in corpus (1)

• Multi-Dimensional Elephant Random Walk with Coupled Memory