A Collection of Stochastic Resonance Examples

Stochastic resonance is a nonlinear phenomenon where the addition of an optimal amount of noise can actually enhance the detection of weak signals. This counterintuitive effect is widely observed in physical, biological, and engineering systems. The following collection presents several classic implementation examples: Bi-stable System Model: The most common stochastic resonance scenario involves a particle in a double-well potential subjected to periodic driving and noise. When noise intensity reaches an optimal level, the particle's transition frequency synchronizes with the driving signal, significantly improving the output signal's signal-to-noise ratio. In MATLAB implementation, this typically requires solving the Langevin equation using ODE solvers like ode45, with parameters for potential barrier height and driving frequency. Neuron Firing Model: In biological neural systems, subthreshold signals can trigger action potentials when combined with random noise. This phenomenon explains why certain sensory systems become more sensitive in noisy environments. Code implementation often involves Hodgkin-Huxley or FitzHugh-Nagumo models with noise injection using randn() function to simulate stochastic channel openings. Mechanical Vibration Detection: In fault diagnosis applications, weak vibration signals from bearings are often淹没 by environmental noise. By designing stochastic resonance filters, characteristic frequency components can be amplified. MATLAB implementations typically involve signal preprocessing using bandpass filters, followed by nonlinear system response analysis through Euler-Maruyama numerical integration. Image Enhancement Applications: Adding controlled noise to low-contrast images followed by nonlinear processing can enhance edge or texture information. Implementation approaches include using imnoise() function for noise addition and morphological operations for nonlinear processing, with careful parameter tuning to avoid excessive noise amplification. In MATLAB implementations, key steps involve: signal generation using sinusoidal functions, noise injection with controlled variance via awgn() function, nonlinear system response analysis through numerical integration of differential equations, and spectral evaluation using fft() and periodogram functions. Critical consideration: noise intensity must remain within the "resonance region" for optimal results - excessive or insufficient noise will degrade performance. Parameter optimization techniques like gradient descent or genetic algorithms can help identify the optimal noise level.