Bifurcation 1D Analysis

BIFURCATION_1D_ANALYZER - tool for getting basic types of bifurcation analysis for nonlinear systems, defined as ODE.

Bifurcation diagram is a commonly used tool to analyze the nonlinear dynamics. It represents the phase space properties of the system, and is often combined with other types of calculations, such as the largest Lyapunov exponent or spectrum, depending on the value of the bifurcation parameter. Also, bifurcation analysis allows studying spiking neuron models based on spike distribution histograms, as well as to find multistability in nonlinear systems using continuation bifurcation diagrams. All of these options are available in this tool.

The presented tool is implemented as MATLAB class bifurcation_1d_analyzer. It also uses a class for arbitrary fixed time step Runge-Kutta method solver rk_solver_explicit, which is in practice more stable solver than standard ode45. It allows using classical methods, such as Euler, RK2 (default), RK4 or some others, as well as to define Butcher tableau for any explicit method.

Examples of the study of some chaotic systems using the capabilities of this tool are given.

References:

1. Karimov, T. I., Druzhina, O. S., Andreev, V. S., Tutueva, A. V., & Kopets, E. E. (2021, January). Bifurcation spectral diagrams: a tool for nonlinear dynamics investigation. In 2021 IEEE Conference of Russian Young Researchers in Electrical and Electronic Engineering (ElConRus), pp. 119-123. DOI: 10.1109/ElConRus51938.2021.9396657
2. Karimov, T., Druzhina, O. ... & Rybin, V. (2022). Sensitivity optimization and experimental study of the long-range metal detector based on chaotic duffing oscillator. Sensors, 22(14), 5212. DOI: 10.3390/s22145212
3. Karimov, T., Druzhina, O., Karimov, A., Tutueva, A., Ostrovskii, V., Rybin, V., & Butusov, D. (2022). Single-coil metal detector based on spiking chaotic oscillator. Nonlinear Dynamics, 107(1), 1295-1312. DOI: 10.1007/s11071-021-07062-2