Building Fixed Point-Free Maps with Memristor

Abstract

A memristor is a two-terminal passive electronic device that exhibits memory of resistance. It is essentially a resistor with memory, hence the name “memristor”. The unique property of memristors makes them useful in a wide range of applications, such as memory storage, neuromorphic computing, reconfigurable logic circuits, and especially chaotic systems. Fixed point-free maps or maps without fixed points, which are different from normal maps due to the absence of fixed points, have been explored recently. This work proposes an approach to build fixed point-free maps by connecting a cosine term and a memristor. Four new fixed point-free maps displaying chaos are reported to illustrate this approach. The dynamics of the proposed maps are verified by iterative plots, bifurcation diagram, and Lyapunov exponents. Because such chaotic maps are highly sensitive to the initial conditions and parameter variations, they are suitable for developing novel lightweight random number generators.

Bifurcation, Hidden Chaos, Entropy and Control in Hénon-Based Fractional Memristor Map with Commensurate and Incommensurate Orders

“…Proof. Substituting the control law (28) into the fractional error map (27), we obtain To confirm the validity of this result, numerical simulations are conducted using MATLAB. The values of the specific parameters chosen are β = 0.98, γ 1 = 0.1, γ 2 = −0.3, γ 3 = 1, and the initial values (e 1 (0), e 2 (0), e 3 (0)) = (−0.1, 0.1, 0.2).…”

“…In practice, discrete chaotic systems offer the advantage of avoiding parameter sensitivity issues present in continuous systems, making them easier to implement using digital hardware circuits [25]. Consequently, there has been a growing realization among researchers of the significance of exploring and understanding discrete memristive maps, leading to promising advancements in understanding the behavior of discrete memristor-based systems and their implications for various applications [26][27][28][29][30]. These studies contribute to exploring the interactions between memristive elements and mathematical functions, providing valuable insights into the dynamics of memristive maps and their potential applications in various fields.…”

Dynamical behavior of memristor-coupled heterogeneous discrete neural networks with synaptic crosstalk

“…[43][44][45][46][47][48][49][50][51] As a result, research on discrete neurons has become a hot topic in recent years. In discrete memristor-coupled neural networks, complex dynamical behaviors have been discovered, including coexisting attractors, [52][53][54][55][56] synchronization transitions, and synchronization coexistence. [57,58] Additionally, Lu et al [59] investigated fractional-order neural networks based on discrete memristors and found that this system exhibits richer dynamical behaviors compared to integer-order neural networks.…”

Dynamical behaviors in discrete memristor-coupled small-world neuronal networks

“…[11] that memristors have unique nonlinearity and memory characteristics, and researchers have constructed different new chaotic systems based on discrete memristor models. [12][13][14][15][16][17][18][19][20] Neuronal networks are able to generate complex dynamical behavior when memristors are applied to the field of neuronal networks, which is beneficial for simulating real biological neuronal networks. A three-order neuron circuit with complex neuromorphic behavior was established by inserting a current-controlled Chua Corsage memristor into a resonator.…”