On the Influence of Noise on the Critical and Oscillatory Behavior of a Predator-Prey Model: Coherent Stochastic Resonance at the Proper Frequency

Noise induced changes in the critical and oscillatory behavior of a Prey-Predator system are studied using power spectrum density and Spectral Amplification Factor (SAF) analysis. In the absence of external noise, the population densities exhibit three kinds of asymptotic behavior, namely: Absorbing State, Fixed Point (FP) and an Oscillatory Regime with a well defined proper (natural) frequency. The addition of noise destabilizes the FP phase inducing a transition to a new OR. Surprisingly, it is found that when a periodic signal is added to the control parameter, the system responds robustly, without relevant changes in its behavior. Nevertheless, the Coherent Stochastic Resonance phenomenon is found only at the proper frequency. Also, a method based on SAF allows us to locate very accurately the transition points between the different regimes. 2 Oscillatory behavior is ubiquitous in all aspects of Nature. For instance, time periodic patterns can be found in problems involving the relation between different species (competition , predator-prey, coexistence, etc) [1,2]. Oscillatory behavior can be also found in spatial dispersion and competition of living or chemical species [2–6], and even in some physiological situations (cardiac and circadian rythms) [7]. Recently, and related to the interplay between oscillations and noise, the phenomenon of stochastic resonance (SR) has been studied in different physical, chemical and biological contexts [8]. In particular, SR has been found to play a relevant role in several problems in biology: mammalian sensory systems, increment of the tactile capacity, visual perception, effects of low fequency and low amplitude electromagnetic fields, etc [9]. Even the problem of coupling among SR units has been studied [10,11]. A related, albeit slightly different phenomenon, is the so called stochastic coherent resonance (SCR) [12]. This phenomenon, that resembles SR, corresponds to a situation where the system shows noise-induced coherent oscillations [13] without an externally applied signal or a discrete component in its spectrum (in this aspect it differs from SR without pariodic forcing as discussed in [14]). Here we analyze the effect of fluctuations on a lattice gas model for a prey-predator system with smart pursuit and escape. Our aim is to analyze the possibility that a SCR-like phenomenon can occur in such a system. Our lattice gas model, which is a variant of the cellular automata proposed by Boccara et. al [15], is defined as follows: a lattice site can be either empty or occupied either by a prey or a predator. Double …