Transitions induced by cross-correlated bounded noises and time delay in a genotype selection model

• Genotype selection model interplay with cross-correlated noises and time delay is investigated.
• Transition induced by cross-correlated bounded noises in the systems is observed.
• As time delay increases, probability distribution transfers from unimodal to bimodal.
• The system undergoes a new transition to four stable states for large correlation time.

We present a numerical investigation of occurrence of transitions in a genotype selection model with time delay, where two bounded noises are cross-correlated. Stationary probability distribution (SPD) function is obtained. It is found that: the multiplicative bounded noise can facilitate the gene separation and it plays a constructive role in the genetic selection progress, while the additive bounded noise suppresses the gene separation. The strong correlation between noises gives a big chance to one type haploid out of the group. Besides, what is more interesting is that the correlation time ττ can induce a new transitions (i.e., the curve of the SPD changes from unimodal to bimodal, and then to four peaks as the correlation time ττ increases).