This study explores the extent to which a display changing periodically in perceptual interpretation through smooth periodic physical changes—an inducer—is able to elicit perceptual switches in an intrinsically bistable distant probe display. Four experiments are designed to examine the coupling strength and bistable dynamics with displays of varying degree of ambiguity, similarity, and symmetry—in motion characteristics—as a function of their locations in visual space. The results show that periodic fluctuations of a remote inducer influence a bistable probe and regulate its dynamics through coupling. Coupling strength mainly depends on the relative locations of the probe display and the contextual inducer in the visual field, with stronger coupling when both displays are symmetrical around the vertical meridian and weaker coupling otherwise. Smaller effects of common fate and symmetry are also found. Altogether, the results suggest that long-range interhemispheric connections, presumably involving the corpus callosum, are able to synchronize perceptual transitions across the vertical meridian. If true, bistable dynamics may provide a behavioral method to probe interhemispheric connectivity in behaving human. Consequences of these findings for studies using stimuli symmetrical around the vertical meridian are evaluated.

^{2}). Each display consisted of 4 light bars (length: 3.14 degrees of visual angle (dva thereafter), width: 0.11 dva) arranged in a diamond shape with invisible corners (Figure 1). Bars oriented at 45° oscillated up and down in phase, while bars oriented at 135° oscillated up and down 90° out of phase with the same amplitude (0.42 dva) and frequency (1 Hz). Under these conditions, each display could be seen as a single diamond-like shape translating along a circular trajectory—a rigid percept—or as four bars translating up and down independently—a non-rigid percept.

*N,*is plotted as a function of the phase duration of state

*N*+ 1. In first return maps, a periodic system is characterized by a single-point attractor of the system, while scattered phase durations are characteristics of a chaotic system. We then derived one-dimensional histograms from first return maps by counting the [

*N, N*+ 1] events in cells of 500 × 500 ms covering the phase space and used these histograms to compute correlation coefficients (

*R*of Bravais–Pearson) across conditions. We expected a dense probability of events around 4 s for the inducer and scattered values for the bistable display. High positive correlations between the bistable/inducer and the inducer/inducer conditions would provide evidence for an effect of the inducer.

*SD*= 9.7) in the bistable condition (Mdn = 6.2 s), 4.5 s (

*SD*= 3) in the direct inductive condition (Mdn = 4 s), and 5.3 s (

*SD*= 4.7) in the indirect inductive condition (Mdn = 4.1 s). These differences are significant for both the mean (

*F*(2, 12) = 9.4,

*p*< 0.005) and median values (

*F*(2, 12) = 11.38,

*p*< 0.002). Post-hoc analyses indicate that mean phase durations are significantly longer for bistable than for direct inductive trials (

*t*(6) = 3.7,

*p*< 0.01) and indirect inductive trials (

*t*(6) = 2.78,

*p*< 0.025). Mean phase durations between the direct and indirect inductive conditions are marginally different (

*t*(6) = 1.92,

*p*= 0.051) in contrast to median values (

*t*(6) = 1.08,

*p*= 0.32). The mean phase durations for both direct and indirect inductive conditions are close to 4 s as expected if the smooth luminance changes drove perceptual alternations.

*F*(1,6) = 2.63,

*p*= 0.16 and

*F*(1,6) < 1, respectively). The median durations were not significantly different between moving/static and moving/moving conditions (

*F*(1,6) < 1), and the mean durations were only marginally different (

*F*(1,6) = 5.37,

*p*= 0.06).

*D*= 0.04,

*p*> 0.2). For the direct induction condition, the raw distribution is bimodal because on some trials observers skipped a transition (as it can be seen in Figure 2B). Taking all phase durations into account does not provide significant fits for any function (Gaussian, lognormal, or gamma). We therefore decided to use phase durations lower than 7000 ms (thus removing 8% of the phase durations). As a result, the direct condition is not different from a Gaussian distribution (one-sampled Kolmogorov–Smirnov:

*D*= 0.03,

*p*> 0.5) but differs from both gamma and lognormal distributions (both

*p*< 0.01). Similarly, taking all phase durations into account, the indirect induction condition is different from Gaussian, lognormal, and gamma distributions. Fitting phase durations lower than 7000 ms, as for direct induction, indicates that the distribution is not significantly different from a Gaussian (one-sampled Kolmogorov–Smirnov:

*D*= 0.03,

*p*> 0.5) but significantly differs from both gamma and lognormal distributions (both

*p*< 0.01).

*D*= 0.46,

*p*< 0.0001) and indirect inductive conditions (two-sampled Kolmogorov–Smirnov:

*D*= 0.31,

*p*< 0.0001). Furthermore, the distributions of the direct and indirect inductive conditions were also significantly different (two-sampled Kolmogorov–Smirnov:

*D*= 0.15,

*p*< 0.0001), but both were well fitted by a Gaussian.

*p*> 0.05). The variance of the temporal delays is significantly higher in the bistable than in the indirect inductive condition for both types of transitions (rigid to non-rigid:

*t*(6) = 11.4,

*p*< 0.0001, one-tailed; non-rigid to rigid:

*t*(6) = 12.4,

*p*< 0.0001, one-tailed). These results suggest that observers tended to switch in phase with the luminance changes in both the direct and indirect conditions. Analyzing further the median of the temporal delays indicated that perceptual switches occurred significantly later in the indirect inductive condition (∼350 ms) than in the direct inductive condition (−113 ms vs. 236 ms:

*t*(6) = 3.16,

*p*< 0.025).

*N,*is plotted against the duration of the following percept

*N*+ 1. As shown in Figure 2D, FRMs pooled across observers yield scattered plots in the bistable condition and highly centered plots in the direct inductive condition. In the indirect inductive condition, the distribution resembles that of the direct inductive condition. In order to compare these distributions, we derived one-dimensional histograms from the FRMs (small squares in Figure 2D; see Methods and stimuli section). We then calculated global correlation coefficients between conditions (all subject data points in one go). The correlation coefficient was 0.20 between the bistable and direct inductive conditions, 0.30 between the bistable and indirect inductive conditions, and 0.76 between the direct inductive and indirect inductive conditions, suggesting that these later conditions share similar perceptual dynamics.

*t*(6) = 2.8,

*p*< 0.03).

*a priori*reason that these factors depend on motion similarity.

*SD*= 1.25) in the S condition, 5.9 s (

*SD*= 1.7) in the O condition, and 7.4 s (

*SD*= 2.3) in the P condition. An ANOVA performed on mean phase durations indicated that these differences are significant (

*F*(2, 12) = 6.1,

*p*< 0.05). Comparing the average phase durations of the S and O conditions yielded no significant differences (

*t*(13) < 1). Average phase durations in the O condition were significantly higher than in the S condition (

*t*(13) = 3.8,

*p*< 0.005). The spatial location, left or right, of the probe display has no significant effect (

*F*(1.6) < 1).

*D*= 0.09,

*p*= 0.084) but differed significantly in the S and P conditions (two-sampled Kolmogorov–Smirnov:

*D*= 0.12,

*p*< 0.01).

*F*(2, 12) < 1) and only marginally significant for rigid to non-rigid (

*F*(2, 12) = 3.3,

*p*= 0.07).

*F*and

*t*values <1).

*per se*.

*F*(2, 22) = 16.5,

*p*< 0.0001). In this global analysis, neither the location of displays in the visual field nor the interaction between condition and location had a significant effect (

*F*(1, 11) < 1 for location;

*F*(2, 22) = 1.02,

*p*< 0.38 for the interaction).

*T*-test:

*t*(11) = −1.8,

*p*= 0.05). Mean phase duration in the indirect inductive condition was significantly shorter than in the bistable condition for bilateral presentation (one-tailed

*T*-test:

*t*(11) = −2.5,

*p*< 0.025). This was not the case for unilateral presentation (one-tailed

*T*-test:

*t*(11) = −1.35,

*p*= 0.10).

*F*(1, 11) = 2,

*p*= 0.18) and the significant effect of the type of induction (

*F*(1, 11) = 28.24,

*p*< 0.005) indicate that phase durations were significantly longer in the indirect inductive condition, but only with unilateral displays, suggesting that the inducer was less influential in this condition. Furthermore, we found a significant interaction effect between display location and the type of induction (Direct/Indirect:

*F*(1, 11) = 5.8,

*p*< 0.05), which corroborates the observation than coupling is reduced in unilateral displays with stimuli in opposite motion direction (Figure 4A).

*D*= 0.08,

*p*= 0.34) and direct inductive conditions (

*D*= 0.07,

*p*= 0.28), while differences were significant in the indirect inductive condition (

*D*= 0.14,

*p*< 0.005).

*T*-test:

*t*(11) < 1) or up/down positions in bilateral configurations (one-tailed

*T*-test:

*t*(11) < 1). This is also true for the distributions of phase durations (Kolmogorov–Smirnov tests; Left/Right:

*D*= 0.06,

*p*= 0.79; Up/Down:

*D*= 0.09,

*p*= 0.15) and for the mean variance of temporal delays (one-tailed

*T*-test: all

*p*> 0.025).

*F*(2, 22) = 51,

*p*< 0.0001; non-rigid to rigid:

*F*(2, 22) = 25.5,

*p*< 0.0001). In contrast to phase duration analysis, neither the location effect (one or two hemispheres) nor the interaction between location and condition was significant, whatever the type of transitions (all

*p*> 0.09).

*T*-test: non-rigid to rigid:

*t*(11) = −4,

*p*< 0.001; rigid to non-rigid:

*t*(11) = −4.6,

*p*< 0.0005). This effect was also found in unilateral presentation for rigid to non-rigid transition (one-tailed

*T*-test:

*t*(11) = −3.5,

*p*< 0.005) but not for non-rigid to rigid transition (one-tailed

*T*-test:

*t*(11) = −1,

*p*= 0.16). Overall, these results suggest that coupling strength is reduced only when stimuli moving in opposite directions are displayed in one hemifield.

*p*> 0.3). However, contrary to all other analyses, median values of phase durations do not yield to the same observation as the mean values, as significant effects, reported below, show up. In unilateral configurations, median phase durations were significantly shorter in the indirect inductive condition compared to bistable conditions when displays have the same direction (one-tailed

*T*-test:

*t*(11) = −2.45,

*p*< 0.025) but were not different with opposite directions (one-tailed

*T*-test:

*t*(11) = −0.7,

*p*= 0.24). Furthermore, Kolmogorov–Smirnov tests on phase duration distribution showed the same differences (same direction:

*D*= 0.15,

*p*< 0.01; opposite direction:

*D*= 0.10,

*p*= 0.2). Overall, these results indicate that motion similarity influenced perceptual coupling more in unilateral displays than in bilateral ones.

*R*= 0.66) compared to unilateral configurations (

*R*= 0.33). Similar differences were found with displays presented in the lower bilateral quadrants (

*R*= 0.61) or in the unilateral right hemifield (

*R*= 0.4). With identical motion direction, the correlations in bilateral (

*R*= 0.60) and unilateral configurations (

*R*= 0.52) remain high.

*T*-test:

*F*(1,12) = 5.3,

*p*< 0.05). No significant interaction was found (

*F*(1,12) < 1). However, comparisons between unilateral and bilateral displays showed a significant difference for stimuli moving in opposite directions (

*t*(11) = −2.5,

*p*< 0.03) but not for displays moving in the same direction (

*t*(11) < 1).

*F*(2,18) = 4.67,

*p*< 0.05). A main effect of motion direction was also found (

*F*(1,9) = 10.23,

*p*< 0.05). The interaction between position and direction was not significant (

*F*(2,18) = 1.2,

*p*= 0.32). The effects of location were more important for a large vertical offset and opposite motion directions, as confirmed by post-hoc pairwise comparisons: Mean phase durations were significantly longer for a full as compared to no vertical offset (

*F*(1,9) = 5.37,

*p*< 0.05). For this comparison, the effect of motion direction is also significant (

*F*(1,9) = 9.43,

*p*< 0.05). Mean phase durations were not significantly different for half and zero vertical offsets (

*F*(1,9) < 1) and only marginally different for motion direction (

*F*(1,9) = 4.37,

*p*= 0.07).

*R*= 0.23) and increased up to 0.5 for symmetrical configurations.

*F*(2,18) = 4,

*p*< 0.05). When comparing only the full deviation to the no deviation condition, an effect of motion direction emerged (

*F*(1,9) = 14.8,

*p*< 0.005), with a remaining effect of the deviation (

*F*(1,9) = 14.5,

*p*< 0.005). Another specific finding showed that there is a significant difference between half-deviation and full deviation when stimuli are moving in opposite directions (

*t*(9) = 2.6,

*p*< 0.03) but not when they are moving in the same direction (

*t*(9) < 1).

*t*(6) = 1.56,

*p*= 0.17 and

*t*(6) = 1,

*p*= 0.35, respectively). A similar analysis was conducted on the number of saccadic eye movements with similar results (

*p*> 0.07 for both horizontal and vertical saccades).

*Oeuvres Complètes*(vol. 1). Paris: Gauthier Villars, 1951).