Search Results (105)

Medical images demand robust privacy protection, driving research into advanced image encryption (IE) schemes. However, current IE schemes still encounter certain challenges in both security and efficiency. Fractional-order Hopfield neural networks (HNNs) demonstrate unique advantages in IE. The introduction of fractional-order calculus operators enables them to possess more complex dynamical behaviors, creating more random and unpredictable keystreams. To enhance privacy protection, this paper introduces a high-performance medical IE scheme that integrates a novel 4D fractional-order HNN with a differentiated encryption strategy (MIES-FHNN-DE). Specifically, MIES-FHNN-DE leverages this 4D fractional-order HNN alongside a 2D hyperchaotic map to generate keystreams collaboratively. This design not only capitalizes on the 4D fractional-order HNN’s intricate dynamics but also sidesteps the efficiency constraints of recent IE schemes. Moreover, MIES-FHNN-DE boosts encryption efficiency through pixel bit splitting and weighted accumulation, ensuring robust security. Rigorous evaluations confirm that MIES-FHNN-DE delivers cutting-edge security performance. It features a large key space ($2^{383}$), exceptional key sensitivity, extremely low ciphertext pixel correlations (<0.002), excellent ciphertext entropy values (>7.999 bits), uniform ciphertext pixel distributions, outstanding resistance to differential attacks (with average NPCR and UACI values of $99.6096\%$ and $33.4638\%$, respectively), and remarkable robustness against data loss. Most importantly, MIES-FHNN-DE achieves an average encryption rate as high as 102.5623 Mbps. Compared with recent leading counterparts, MIES-FHNN-DE better meets the privacy protection demands for medical images in emerging fields like medical intelligent analysis and medical cloud services. Full article

In a biological nervous system, neurons are connected to each other via synapses to transmit information. Synaptic crosstalk is the phenomenon of mutual interference or interaction of neighboring synapses between neurons. This phenomenon is prevalent in biological neural networks and has an important impact on the function and information processing of the neural system. In order to simulate and study this phenomenon, this paper proposes a memristor model based on hyperbolic tangent function for simulating the activation function of neurons, and constructs a three-neuron HNN model by coupling two memristors, which brings it close to the real behavior of biological neural networks, and provides a new tool for studying complex neural dynamics. The intricate nonlinear dynamics of the MHNN are examined using techniques like Lyapunov exponent analysis and bifurcation diagrams. The viability of the MHNN is confirmed through both analog circuit simulation and FPGA implementation. Moreover, an image encryption approach based on the chaotic system and a dynamic key generation mechanism are presented, highlighting the potential of the MHNN for real-world applications. The histogram shows that the encryption algorithm is effective in destroying the features of the original image. According to the sensitivity analysis, the bit change rate of the key is close to 50% when small perturbations are applied to each of the three parameters of the system, indicating that the system is highly resistant to differential attacks. The findings indicate that the MHNN displays a wide range of dynamical behaviors and high sensitivity to initial conditions, making it well-suited for applications in neuromorphic computing and information security. Full article

Despite its significance, hysteresis remains underrepresented in mainstream models of plasticity. In this work, we propose a novel framework that explicitly models hysteresis in simple one- and two-neuron models. Our models capture key feedback-dependent phenomena such as bistability, multistability, periodicity, quasi-periodicity, and chaos, offering a more accurate and general representation of neural adaptation. This opens the door to new insights in computational neuroscience and neuromorphic system design. Synaptic weights change in several contexts or mechanisms including, Bienenstock–Cooper–Munro (BCM) synaptic modification, where synaptic changes depend on the level of post-synaptic activity; homeostatic plasticity, where all of a neuron synapses simultaneously scale up or down to maintain stability; metaplasticity, or plasticity of plasticity; neuromodulation, where neurotransmitters influence synaptic weights; developmental processes, where synaptic connections are actively formed, pruned and refined; disease or injury; for example, neurological conditions can induce maladaptive synaptic changes; spike-time dependent plasticity (STDP), where changes depend on the precise timing of pre- and postsynaptic spikes; and structural plasticity, where changes in dendritic spines and axonal boutons can alter synaptic strength. The ability of synapses and neurons to change in response to activity is fundamental to learning, memory formation, and cognitive adaptation. This paper presents simple continuous and discrete neuro-modules with adapting feedback synapses which in turn are subject to feedback. The dynamics of continuous periodically driven Hopfield neural networks with adapting synapses have been investigated since the 1990s in terms of periodicity and chaotic behaviors. For the first time, one- and two-neuron models are considered as parameters are varied using a feedback mechanism which more accurately represents real-world simulation, as explained earlier. It is shown that these models are history dependent. A simple discrete two-neuron model with adapting feedback synapses is analyzed in terms of stability and bifurcation diagrams are plotted as parameters are increased and decreased. This work has the potential to improve learning algorithms, increase understanding of neural memory formation, and inform neuromorphic engineering research. Full article

The human brain is an extremely sophisticated system. Several neural models have been proposed to mimic and understand brain function. Most of them incorporate memristors to simulate autapse or self-coupling, electromagnetic radiation and the synaptic weight of the neuron. This article introduces and studies the dynamics of a Hopfield neural network (HNN) consisting of four neurons, where one of the synaptic weights of the neuron is replaced by a memristor. Theoretical aspects such as dissipation, the requirements for the existence of attractors, symmetry, equilibrium states and stability are studied. Numerical investigations of the model reveal that it develops very rich and diverse behaviors such as chaos, hyperchaos and transient chaos. These results obtained numerically are further supported by the results obtained from an electronic circuit of the system, constructed and simulated in PSpice. Both approaches show good agreement. In light of the findings from the numerical and experimental studies, it appears that the 4D Hopfield neural network under consideration in this work is more complex than its original version, which did not include a memristor. Full article

This paper is concerned with the event-based synchronization control for chaotic neural networks by using a refined discontinuous trigger scheme. To get rid of the Zeno phenomenon and decrease the triggering times, a refined discontinuous event-trigger (RDET) scheme is employed by designing a new threshold function. The proposed threshold function consists of two parts, i.e., quadratic term and exponential decay term, which makes the derivative of the Lyapunov function possibly not less than zero. On this basis, an important lemma is derived, which contributes to performing a stability analysis. Then, the corresponding closed-loop system model is established in the presence of a trigger scheme. Then, a time-dependent Lyapunov function (TLF) method is established based on the features of an RDET. In view of inequality estimation techniques and stability theory, some synchronization criteria are developed to guarantee that the synchronization of chaotic neural networks can be realized by using the novel discontinuous event-trigger schemes. Finally, a Hopfield neural network is displayed to demonstrate the advantages and effectiveness of the derived results. Full article

This work establishes a simple algorithm to recover an information vector from a predefined database available every time. It is considered that the information analyzed may be incomplete, damaged, or corrupted. This algorithm is inspired by Hopfield Neural Networks (HNN), which allows the recursive reconstruction of an information vector through an energy-minimizing optimal process, but this paper presents a procedure that generates results in a single iteration. Images have been chosen for the information recovery application to build the vector information. In addition, a filter is added to the algorithm to focus on the most important information when reconstructing data, allowing it to work with damaged or incomplete vectors, even without losing the ability to be a non-iterative process. A brief theoretical introduction and a numerical validation for recovery information are shown with an example of a database containing 40 images. Full article

This study develops an MTSP model for multi-UAV delivery optimization from a central hub, proposing a hybrid algorithm that integrates genetic simulated annealing-enhanced clustering with an improved Hopfield neural network to minimize the total flight distance. The proposed methodology initially employs an enhanced fuzzy C-means clustering technique integrated with genetic simulated annealing (GSA) to effectively partition the MTSP formulation into multiple discrete traveling salesman problem (TSP) instances. The subsequent phase implements an enhanced Hopfield neural network (HNN) architecture incorporating three key modifications: data normalization procedures, adaptive step-size control mechanisms, and simulated annealing integration, collectively improving the TSP solution quality and computational efficiency. The proposed algorithm’s effectiveness is validated through comprehensive case studies, demonstrating significant performance improvements in the computational efficiency and solution quality compared to conventional methods. The results show that during clustering, the improved clustering algorithm is more stable in its clustering effect. With regard to path optimization, the improved neural network algorithm has a higher computational efficiency and makes it easier to obtain the global optimal solution. Compared with the genetic algorithm and ant colony algorithm, its iteration times, path length, and delivery time are reduced to varying degrees. To sum up, the hybrid optimization algorithm has obvious advantages for solving a multi-UAV collaborative distribution path optimization problem. Full article

In this digital era, social images are the most vital information carrier on multimedia social platforms. More and more users are interested in sharing social images with mobile terminals on multimedia social platforms. Social image sharing also faces potential risks from malicious use, such as illegal sharing, piracy, and misappropriation. This paper mainly concentrates on secure social image sharing. To address how to share social images in a safe way, a social image security scheme is proposed. The technology addresses the social image security problem and the active tracing problem. First, discrete wavelet transform (DWT) is performed directly from the JPEG image. Then, the high-bit planes of the LL, LH, and HL are permuted with cellular automation (CA), bit-XOR, and singular value decomposition (SVD) computing, and their low-bit planes are chosen to embed a watermark. In the end, the encrypted and watermarked image is again permuted with cellular automation in the discrete cosine transform (DCT) domain. Experimental results and security analysis show that the social image security method not only has good performance in robustness, security, and time complexity but can also actively trace the illegal distribution of social images. The proposed social image security method can provide double-level security for multimedia social platforms. Full article

This manuscript introduces a simple third-order Hopfield neural network. Its dynamics, implementation with a microcontroller and application to random number generation are explored. The model includes three coupled neurons with no synaptic weights between the first neuron and the third, and between the third and the second. The fundamental features (i.e., symmetry, dissipation and the requirement of existence of an attractor) of the model are studied. The results suggest that the model is asymmetric, dissipative and capable of supporting attractors. The dynamic analysis of the model is conducted through computer explorations, and the findings reveal that it develops complex behaviors like chaos and the coexistence of patterns. The coexistence of patterns is controlled using the linear augmentation method. The coexisting patterns are destroyed, and the multistable system is transformed into a monostable one. In order to confirm the numerical findings, a microcontroller implementation of the considered HNN model is carried out, and the findings of both approaches are concordant. Finally, the elaborated third-order HNN chaotic model is designed for random number generation application. The NIST statistical tests are provided in order to confirm the random features of the generated signals. Full article

Neurons in the brain are interconnected through synapses. Local active memristors can both simulate the synaptic behavior of neurons and the action potentials of neurons. Currently, the hyperbolic tangent function-type memristors used for coupling neural networks do not belong to local active memristors. To take advantage of local active memristors and consider the multi-equilibrium point problem, a cosine function is introduced into the state equation, resulting in the design of an absolute value hyperbolic tangent-type double local active memristor, and it is used as a coupling synapse to replace a synaptic weight in a 3-neuron HNN. Then, basic dynamical analysis methods are used to study the effects of different memristor synapse coupling strengths and different initial conditions on the dynamics of the neural network. The research results indicate that dynamical behavior of memristor Hopfield neural network is closely related to the synaptic coupling strengths and the initial conditions, and this neural network exhibits rich dynamical behaviors, including the coexistence of chaotic and periodic attractors, super-multistability phenomena, etc. Finally, the neural network was implemented using an FPGA development board, verifying the hardware feasibility of this system. Full article

Locally active memristors with an Edge-of-Chaos kernel (EOCK) represent a significant advancement in the simulation of neuromorphic dynamics. However, current research on memristors with an EOCK remains at the circuit level, without further analysis of their feasibility. In this context, we designed a memristor and installed it in a third-order circuit, where it showed local activity and stability under defined voltage and inductance parameters. This behavior ensured that by varying the input voltage and inductance, the memristor could effectively simulate various neural activities, including inhibitory postsynaptic potential and chaotic waveforms. By subsequently integrating the memristor with an EOCK into a Hopfield neural network (HNN) framework and substituting the self-coupling weight, we observed a rich spectrum of dynamic behaviors, including the rare phenomenon of antimonotonicity bubble bifurcation. Finally, we used hardware circuits to realize these generated dynamic phenomena, confirming the feasibility of the memristor. By introducing the HNN and studying its dynamic behavior and hardware circuit implementation, this study provides theoretical insights into and an empirical basis for developing circuits and systems that replicate the complexity of human brain functions. This study provides a reference for the development and application of EOCK in the future. Full article

The Hopfield Recurrent Neural Network (HRNN) is a single-point descent metaheuristic that uses a single potential solution to explore the search space of optimization problems, whose constraints and objective function are aggregated into a typical energy function. The initial point is usually randomly initialized, then moved by applying operators, characterizing the discrete dynamics of the HRNN, which modify its position or direction. Like all single-point metaheuristics, HRNN has certain drawbacks, such as being more likely to get stuck in local optima or miss global optima due to the use of a single point to explore the search space. Moreover, it is more sensitive to the initial point and operator, which can influence the quality and diversity of solutions. Moreover, it can have difficulty with dynamic or noisy environments, as it can lose track of the optimal region or be misled by random fluctuations. To overcome these shortcomings, this paper introduces a population-based fuzzy version of the HRNN, namely Gaussian Takagi–Sugeno Hopfield Recurrent Neural Network (G-TS-HRNN). For each neuron, the G-TS-HRNN associates an input fuzzy variable of d values, described by an appropriate Gaussian membership function that covers the universe of discourse. To build an instance of G-TS-HRNN(s) of size s, we generate s n-uplets of fuzzy values that present the premise of the Takagi–Sugeno system. The consequents are the differential equations governing the dynamics of the HRNN obtained by replacing each premise fuzzy value with the mean of different Gaussians. The steady points of all the rule premises are aggregated using the fuzzy center of gravity equation, considering the level of activity of each rule. G-TS-HRNN is used to solve the random optimization method based on the support vector model. Compared with HRNN, G-TS-HRNN performs better on well-known data sets. Full article

Memristor-based fractional-order chaotic systems can record information from the past, present, and future, and describe the real world more accurately than integer-order systems. This paper proposes a novel memristor model and verifies its characteristics through the pinched loop (PHL) method. Subsequently, a new fractional-order memristive Hopfield neural network (4D-FOMHNN) is introduced to simulate induced current, accompanied by Caputo’s definition of fractional order. An Adomian decomposition method (ADM) is employed for system solution. By varying the parameters and order of the 4D-FOMHNN, rich dynamic behaviors including transient chaos, chaos, and coexistence attractors are observed using methods such as bifurcation diagrams and Lyapunov exponent analysis. Finally, the proposed FOMHNN system is implemented on a field-programmable gate array (FPGA), and the oscilloscope observation results are consistent with the MATLAB numerical simulation results, which further validate the theoretical analysis of the FOMHNN system and provide a theoretical basis for its application in the field of encryption. Full article

Systems of incommensurate delay fractional differential equations (DFDEs) with non-vanishing constant delay of retarded type are investigated. It is shown that the mild solutions are well-posed in Hadamard sense on the space of continuous functions. The analysis is local and carried out for finite intervals. The strong results are obtained with weak conditions by using state-of-the-art new methods. No condition on the Lipschitz parameter is added for well-posedness results. Application of this theorem for the Hopfield neural network is carried out. Full article

Memristors have become important components in artificial synapses due to their ability to emulate the information transmission and memory functions of biological synapses. Unlike their biological counterparts, which adjust synaptic weights, memristor-based artificial synapses operate by altering conductance or resistance, making them useful for enhancing the processing capacity and storage capabilities of neural networks. When integrated into systems like Hopfield neural networks, memristors enable the study of complex dynamic behaviors, such as chaos and multistability. Moreover, fractional calculus is significant for their ability to model memory effects, enabling more accurate simulations of complex systems. Fractional-order Hopfield networks, in particular, exhibit chaotic and multistable behaviors not found in integer-order models. By combining memristors with fractional-order Hopfield neural networks, these systems offer the possibility of investigating different dynamic phenomena in artificial neural networks. This study investigates the dynamical behavior of a fractional-order Hopfield neural network (HNN) incorporating a memristor with a piecewise segment function in one of its synapses, highlighting the impact of fractional-order derivatives and memristive synapses on the stability, robustness, and dynamic complexity of the system. Using a network of four neurons as a case study, it is demonstrated that the memristive fractional-order HNN exhibits multistability, coexisting chaotic attractors, and coexisting limit cycles. Through spectral entropy analysis, the regions in the initial condition space that display varying degrees of complexity are mapped, highlighting those areas where the chaotic series approach a pseudo-random sequence of numbers. Finally, the proposed fractional-order memristive HNN is implemented on a Field-Programmable Gate Array (FPGA), demonstrating the feasibility of real-time hardware realization. Full article