Dynamical mechanism behind ghosts unveiled in a map complexification

Canela, Jordi; Alsedà, Lluı́s; Fagella, Núria; Sardanyés, Josep

doi:10.1016/j.chaos.2021.111780

Cited by 5 publications

(3 citation statements)

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“…This collision produces a bottleneck which hugely delays the dynamics in the deterministic system for suitable initial conditions. S-n bifurcations typically arise in biological dynamical systems with strong nonlinearities such as cooperation (both intra-or interspecific) [9,11,12,[14][15][16]. For instance, intra-specific cooperation is found in several species including social insects [17,18], marine species [19], bats [17] and primates [20].…”

Section: Introductionmentioning

confidence: 99%

“…Ghosts have been thoroughly analysed in deterministic systems [3,5,[12][13][14][15][16][24][25][26][27]. However, recent computational studies have addressed the effects of intrinsic noise, i.e.…”

Section: Introductionmentioning

confidence: 99%

“…In this bifurcation, the equilibrium points collide and get annihilated, as the colliding equilibria move to the complex domain (double-struckC) after crossing the bifurcation [3,10–13]. Recent research has explored the dynamical mechanisms taking place at the complex phase space (in general, in Cn) causing such slowdown in transients [14]. These delays are usually referred to as delayed transitions or ghosts [3,5].…”

Section: Introductionmentioning

confidence: 99%

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Semiclassical theory predicts stochastic ghosts scaling

et al. 2023

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Slowing down occurs in dynamical systems close to bifurcations or phase transitions. The time length ( τ ) of ghost transients close to a saddle-node bifurcation in deterministic systems follows τ ∼ | ϵ − ϵ c | − 1 / 2 , ϵ being the bifurcation parameter and ϵ c its critical value. Recently, we numerically investigated how intrinsic noise affected the deterministic picture, finding a more complicated scaling law. We here provide a theoretical basis for this new law with two models of cooperation using a Wentzel–Kramers–Brillouin asymptotic approximation of the Master Equation. A study of the phase space of the Hamiltonian derived from the Hamilton–Jacobi equation shows that the statistically significant orbits (paths) reproduce the scaling function observed in the stochastic simulations. The flight times tied to these orbits underpin the scaling law of the stochastic system, and the same properties should extend in a universal way to all stochasticsystems whose associated Hamiltonian exhibits the same behaviour. Our approach allows to make useful theoretical predictions of transient times in stochastic systems close to a bifurcation.

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