In this study, a total of six adult homing pigeons (Columba livia, 450–500 g, unknown sex) obtained from a local supplier (Gongchuang Pigeon Co., Zhengzhou, Henan, China) were used. All pigeons were housed in a loft, provided with regular feeding by professionals and free drinking water in their normal living conditions. The pigeons’ diet was restricted during flight tasks until completion of the experiment. All experimental procedures adhered to the guidelines outlined in the Animals Act, 2006 (China), and aimed to ensure the ethical care and use of laboratory animals. The study protocol was approved by the Life Science Ethical Review Committee of Zhengzhou University (No. SYXK 2019-0002).

Once it was established that the pigeons were capable of reliably completing the flight task, we implanted microelectrode arrays into the FRM of pigeons, in which eight individually insulated tungsten microwires (California Fine Wire, Grover Beach, CA, USA) with a 35-µm inner diameter and 150-µm spacing between the wires (Kedou Brain Computer Technology, Suzhou, Jiangsu, China) were used. The surgical procedure followed a similar protocol as described in our previous study [20]. Initially, pigeons were anesthetized using a 3% sodium pentobarbitone solution (at a dose of 0.12 mL/100 g body weight, C${}_{11}$H${}_{17}$N${}_2$NaO${}_3$, Shanghai Toscience Biotechnology Co., Ltd, Shanghai, China) and securely placed in a stereotaxic apparatus. Next, the location of the FRM was determined using a stereotactic map of the pigeon brain [21] as a guide. Finally, the 8-channel microelectrode array (Customized version, Kedou Co., Suzhou, Jiangsu, China) was implanted into the target point with the following coordinates: anteroposterior (AP) 3.60 mm, mediolateral (ML) 1.20 mm, and dorsoventral (DV) 8.10 mm. The specific position of the electrode implantation and the pigeon after the implantation are shown in Fig. 1A,B, respectively.

To simultaneously record the flight state related GPS data of pigeons and their neural signals in the FRM, a wearable data recording device was developed, which was described extensively in our previous publication [19] and is shown in Fig. 1C. The self-made device (Henan Key Laboratory of Brain Science and Brain-Computer Interface Technology, Zhengzhou, Henan, China) weighed 13.6 g and consisted of a GPS module (ATGM336H-5N with sampling range of 1–10 Hz, positional accuracy 2.5 m circular error probable) and a neural signal acquisition module (8-channel ADS1299 from Texas Instruments (ADS1299IPAGR, TI Co., Dallas, TX, USA) with sampling rate range of 0.25–16 KHz, magnification 1–24, and conversion accuracy 0.1 µV/bit). It should be noted that the GPS data were used for the definition of the typical flight states of pigeons.

Before recording, the pigeons were trained to perform in the study by wearing backpacks to increase their capacity for bearing weight for 2 weeks. The study mainly consisted of a pre-experiment and a formal experiment. In the first week, the pigeons were loaded with 20-g weight during both walking and flying to adapt to the burden of the device. In the second week, the pigeons were released daily on short-distance (2 km) flights away from the loft. After the pre-experiment, the pigeons wore our data recording device as shown in Fig. 1D. During the whole flight process, including baseline, accelerated take-off, uniform flight, and decelerated landing, 8-channel neural signals and GPS data were recorded synchronously as depicted in Fig. 1E.

We performed GPS and LFP data acquisition during the flight of pigeons from the release site to the home loft as shown in Fig. 2. The sampling rate of GPS data is 10 Hz and that of the LFP signal is 1000 Hz. The GPS data provides essential information regarding the pigeon’s latitude and longitude coordinates during free-flying, as well as velocity data. The acceleration of the pigeon during flight can be further calculated based on the velocity data as follows:

(1)$$a=\frac{dv}{dt}$$

When pigeons are flying outdoors, the neural signals can be prone to interference from baseline drift and noise generated by their flapping wings. To address these challenges, it is important to eliminate the trend terms from the neural signals and account for the non-stationary nature of the signal. Firstly, to accomplish baseline drift, discrete wavelet transform (DWT) was employed. The DWT is defined as follows:

(2)$$W_{\phi }f(j,k)=\int s(t){\phi }_{j,k}^{*}(t)𝑑t$$

where $s\left(t\right)$ is the temporal neural signal, ${\phi }_{j,k}\left(t\right)={\mathrm{\hspace{0.25em}2}}^{-\frac{i}{2}}\phi (2^{-j}t-k)$ is the base function, $i$is the frequency resolution, and $j$ is the time shift. In this study, we performed a 10-layer discrete wavelet decomposition to process the original signal using the ‘sym8’ wavelet packet. We then reconstructed the 2–250 Hz sub-band signals to obtain the targeted LFPs without the baseline drift.

To address the issue of flapping noise in the neural signals, the primary method used is priori variational modal decomposition (VMD). This technique aims to extract intrinsic mode functions or modes of oscillation from the signal without relying on fixed functions for analysis. This makes it particularly effective for processing non-smooth and non-linear neural signals. The fundamental concept behind VMD is to construct and solve variational problems [22]. Previous studies have indicated that pigeons exhibit vibrations in the frequency range of approximately 3–10 Hz during flight [23, 24]. According to this prior knowledge, modal components within this frequency range are discarded. The remaining modal components are then reconstructed to obtain the processed LFP signal. In the current study, our multi-channel LFPs were filtered using a zero-phase bandpass filter to obtain signals in the following four frequency bands: $\beta$ (12–30 Hz), ${\gamma }_1$ (30–80 Hz), ${\gamma }_2$ (80–150 Hz), ${\gamma }_3$ (150–250 Hz).

In this study, we focused on four typical flight states of pigeons: baseline, accelerated take-off, uniform flight, and decelerated landing. Previous studies have commonly used GPS speeds greater than 5 or 10 km/h to identify pigeons in flight [25, 26]. However, in this study, we considered the actual movement of the pigeons during flight and the accuracy of the sensors to define the above typical states. For small fluctuations in speed within a certain range ($\pm$0.3 m/s), we considered the pigeon to be flying at a constant speed. For take-off and landing states, we define them using flight speed and acceleration considering their observed significant changes. The state “uniform flight” refers to a state of constant speed flight. This approach acknowledges the agility and flexibility of pigeons in controlling their flight speed. Based on these considerations, the following principles were used to define the four motion states:

(1) Baseline: This state represents a continuous process in which the pigeon’s speed is less than 3 m/s. It typically corresponds to the pigeon being at rest on the ground.

(2) Accelerated take-off: This state represents a continuous process in which the pigeon’s speed is greater than 3 m/s, and the acceleration is greater than 0.6 $m/s^2$. It signifies the pigeon’s initial acceleration during take-off.

(3) Uniform flight: This state represents a continuous process in which the pigeon’s speed is greater than 3 m/s, and the absolute value of the acceleration is less than 0.6 $m/s^2$. It indicates the pigeon’s consistent flight at a relatively constant speed.

(4) Decelerated landing: This state represents a continuous process in which the pigeon’s speed is greater than 3 m/s, and the acceleration is less than –0.6 $m/s^2$. It corresponds to the pigeon’s gradual deceleration during landing.

We then explored the connectivity between multiple channel LFPs in the FRM to find effective features on the scale of local network connections for decoding the four states. This is accomplished by generating a connection matrix that represents the relationship between different channels or brain regions. Subsequently, the topological properties of the brain function connectivity network are analyzed using principles from graph theory. In this study, the connectivity network was established by quantifying the coherence between channels. The coherence coefficient is calculated as follows:

(3)$$C_{xy}^2(f)=\frac{{\left|S_{xy}(f)\right|}^2}{S_{xx}(f)*S_{yy}(f)}$$

where $S_{xy}$ is the cross-power spectral density of signals $x\left(t\right)$ and $y\left(t\right)$, and $S_{xx}$ and $S_{yy}$ are their self-power spectral densities, respectively.

To measure the topological characteristics of the connectivity network, the clustering coefficient (Cc), global efficiency (Ge), and average path length (Apl) were calculated specifically. The clustering coefficient quantifies the tendency for neighboring channels to form interconnected clusters [27]. It provides a measure to evaluate the level of network integration and can be defined as follows:

(4)$$C_c=\frac{1}{N}{\sum }_{i=1}^N{C}_i=\frac{1}{N}{\sum }_{i=1}^N\frac{2E_i}{k_i\left(k_i-1\right)}$$

where N represents the total number of nodes in the network, $k_i$ is the node degree (number of connections) of node $i$, and $E_i$ denotes the total number of triangles formed by the neighbors of node $i$. A larger clustering coefficient suggests that nearby neurons have a higher likelihood of being connected, creating tightly-knit groups within the network.

The global efficiency provides insights into the efficiency of information flow across the network and is defined as the average value of the path length between two nodes in the network as follows:

(5)$$G_e=\frac{2}{N*(N-1)}{\sum }_{i,j\in V,i\ne j}\frac{1}{d_{ij}}$$

where$N$ represents the total number of nodes in the network and $d_{ij}$ represents the path length between node $i$ and node $j$. The higher the global efficiency, the more efficiently the information is transferred between different channels.

The average path length represents the average number of edges required to traverse between any two channels in the network. It provides a measure of the global efficiency of information transmission or integration across the entire network and can be defined as:

(6)$$L=\frac{2}{N(N-1)}{\sum }_{i,j\in V,i\ne j}{d}_{ij}$$

where $d_{ij}$ represents the path length between node $i$ and node $j$. A smaller average path length indicates that there are shorter and more direct pathways between different channels, facilitating efficient information exchange.

We analyzed the differences in connectivity characteristics of the four typical states and extracted effective features for the decoding analysis. Support vector machine (SVM) models can better solve the problem of small sample classification and have been successfully applied in many fields [28]. Thus, an SVM was used in this study for typical flight state decoding and the performance was assessed through ten-fold cross-validation.

Our results are given in the form of mean $\pm$ standard deviation (SD) unless otherwise specified. The statistical differences between different groups or conditions were evaluated using the Kruskal-Wallis test, which is a non-parametric test method. The significance level for determining statistical significance was set at 5% and p-values were considered statistically significant as follows: * p 0.05, ** p 0.01, *** p 0.001.

We effectively collected the data of three pigeons (P02, P03, and P06), while three other animals (P01, P04, and P05) dropped out of the study due to electrode implantation failure or poor signal quality. The pigeons were released from a location about 2 km away from the loft, and one whole flight process recorded by GPS data of P02 is shown in Fig. 2A. The speed and acceleration information of pigeons was calculated based on the GPS data to better characterize their specific states. Four typical motion states including baseline, accelerated take-off, uniform flight, and decelerated landing were then defined according to the above calculations, which are shown in Fig. 2B.

For the recorded neural signals, we have shown a pre-processing example of 5 s of data during the study of P02. Fig. 3A shows the raw signal obtained from one of the acquired channels, in which there is a baseline drift. We then applied the DWT to remove the drift, and the result is shown in Fig. 3B. Fig. 3C shows the time-frequency analysis results of the LFPs, and there is a noticeable wing coupling component with a frequency range of approximately 5–10 Hz. Next, we employed VMD to mitigate the wing-flapping noise; Fig. 3D displays the signal and time-frequency analysis results after VMD.

Each pigeon underwent a different number of sessions, with 12, 13, and 15 sessions respectively in the current study (each session represents one flight experiment). According to the definition of the typical states, we obtained the corresponding neural signals and divided them into segments of 500 ms windows. Table 1 shows the experimental data for three pigeons.

We first compared the results of the power spectrum analysis at different frequency bands in four typical states and the results are shown in Fig. 4A. We observed distinct power spectrum differences among these four typical states, with the most notable discrepancies occurring in the ${\gamma }_2$ band, followed by the ${\gamma }_1$ band, $\beta$ band, and ${\gamma }_3$ band. Thus, we constructed a distribution diagram for the functional network topology characteristics in the ${\gamma }_2$ band of P02 shown in Fig. 4B, in which the subgraph along the diagonal represents the probability density of each feature and the other subgraphs represent the feature distribution between characteristics. The four typical states show distinguishable density distributions from each other, especially for the clustering coefficient and the global efficiency. Specifically, the mean value of the characteristic probability density is highest for the accelerated take-off state and lowest for the baseline state across all three characteristics. Furthermore, from the visualization results that consider the distribution of two-dimensional topological characteristics, we identified clear separability among multiple states. Specifically, the baseline state can be completely distinguished from the other three states in all cases. Between the remaining three states, there are relatively clear classification boundaries observed between the accelerated take-off and uniform flight states, and decelerated landing, while the distributions of the decelerated landing states appear to be partially overlapping between them.

We then calculated the clustering coefficient, global efficiency, and average path length of the functional networks for the four states of three experimental pigeons using graph theory. The statistical analysis results of the clustering coefficient for the bands are shown in Fig. 4C. For the inter-state comparisons, it is apparent that the clustering coefficients for all three typical flight states of the three pigeons are significantly higher (Kruskal-Wallis test, p 0.001) than that during the baseline state in the vast majority of cases (except for the baseline versus the uniform flight and decelerated landing states in the $\beta$ band; Kruskal-Wallis test, p $>$ 0.05). This implies that the brain exhibits a higher level of network integration for effective information transmission during flying. Furthermore, the analysis reveals that the functional connectivity is tighter during state-shifting of flight including the accelerated take-off and decelerated landing states compared with uniform flight, especially for all pigeons in the ${\gamma }_2$ band (Kruskal-Wallis test, p 0.001). This suggests a frequency-specific neural mechanism to encode the transitional phases during flight. For the inter-band comparisons, the characteristics of the ${\gamma }_2$ band demonstrate significant differences across all four states and for all three pigeons (Kruskal-Wallis test, p 0.05). This suggests that the ${\gamma }_2$ band may contribute to the distinct neural patterns for shifting among different states. Finally, it should be noted that we observed identical or similar results in the inter-state statistical analysis of the other two topological characteristics.

The functional connectivity characteristics from the FRM showed variability across four typical states. We therefore sought to ascertain with what accuracy could the pigeon’s current states during flight be determined based on the functional connectivity features. To answer this question, a multi-classified SVM was used to decode the pigeon’s states and the analysis results are shown in Fig. 5 (detailed results are shown in Supplementary Table 1). The typical flight state decoding accuracy of three pigeons is shown in Fig. 5A. The results indicate that the accuracy varies across the four different frequency bands. The best average decoding results for P02 and P06 are achieved in the ${\gamma }_2$ band (0.86 and 0.78), while the highest accuracy for P03 is observed in the ${\gamma }_3$ band (0.81). When considering the overall decoding accuracy using the fused feature set including features in all four bands, P02, P03, and P06 achieve average accuracies of 0.89, 0.84, and 0.86, respectively. This suggests that flight related information of the pigeon could be encoded via specific bands in the FRM and could be decoded by the corresponding neural patterns in these bands.

The statistical decoding results across all three pigeons are shown in Fig. 5B. We observed the best decoding performance using all features in the four bands across the three pigeons, which was significantly higher than those using the features in other single frequency bands (0.86 $\pm$ 0.12 versus 0.66 $\pm$ 0.16, 0.75 $\pm$ 0.16, 0.79 $\pm$ 0.13, 0.65 $\pm$ 0.19; Kruskal-Wallis test, p 0.05). For the performance using the features in the ${\gamma }_2$ band, the average decoding accuracy for the states was significantly higher than those using the features in the $\beta$ band (0.79 $\pm$ 0.13 versus 0.66 $\pm$ 0.16; Kruskal-Wallis test, p 0.001) and the ${\gamma }_3$ band (0.79 $\pm$ 0.13 versus 0.65 $\pm$ 0.19; Kruskal-Wallis test, p 0.01). Similarly, the average accuracy using the features in the ${\gamma }_1$ band was also significantly higher than those in the $\beta$ band (0.75 $\pm$ 0.16 versus 0.66 $\pm$ 0.16; Kruskal-Wallis test, p 0.05) and the ${\gamma }_3$ band (0.75 $\pm$ 0.16 versus 0.65 $\pm$ 0.19; Kruskal-Wallis test, p 0.05). There was no significant difference between the performance of the ${\gamma }_2$ band and ${\gamma }_1$ band (0.79 $\pm$ 0.13 versus 0.75 $\pm$ 0.16; Kruskal-Wallis test, p $>$ 0.05). These findings demonstrate that the ${\gamma }_2$ band and ${\gamma }_1$ band consistently showed relatively high state decoding accuracy across the three pigeons. This may suggest that these frequency bands contain the most relevant encoding information related to the pigeon’s flight. In addition, we also compared the typical flight states decoding results of the three pigeons using LFP power features (detailed results are shown in Supplementary Table 2). The best decoding performance using all features and the superior results in the ${\gamma }_2$ band were also observed.