The laser differential equations are used to transform them into identical coupled maps. Valuable results are deduced during analytical and numerical studies on cavity loss. Phase and spatiotemporal synchronized attractors are observed via quasi-chaos under a certain range of controlling parameters, and symmetry breaking of chaotic attractors due to collision with their basin boundaries, and transpire differently from the previous attractors. During the numerical simulation, it is found that the sequence of repeated strange attractors if the coupling strength further increases, which are orthogonal mirror images (the dynamics of the system is the same at different values of controlling parameters). Moreover, it can help us to predict future problems and their solutions based on current issues, if we develop this model in more general.

The challenge of this work is to re-define the concept of intelligent agent as a building block of social networks by presenting it as a physical particle with additional non-Newtonian properties. The proposed model of an intelligent agent described by a system of ODE coupled with their Liouville equation has been introduced and discussed. Following the Madelung equation that belongs to this class, non-Newtonian properties such as superposition, entanglement, and probability interference typical for quantum systems have been described. Special attention was paid to the capability to violate the second law of thermodynamics, which makes these systems neither Newtonian, nor quantum. It has been shown that the proposed model can be linked to mathematical models of livings as well as to models of AI. The model is presented in two modifications. The first one is illustrated by the discovery of a stochastic attractor approached by the social network; as an application, it was demonstrated that any statistics can be represented by an attractor of the solution to the corresponding system of ODE coupled with its Liouville equation. It was emphasized that evolution to the attractor reveals possible micro-mechanisms driving random events to the final distribution of the corresponding statistical law. Special attention is concentrated upon the power law and its dynamical interpretation: it is demonstrated that the underlying micro- dynamics supports a “violent reputation” of the power-law statistics. The second modification of the model of social network associated with a decision-making process and applied to solution of NP-complete problems known as being unsolvable neither by classical nor by quantum algorithms. The approach is illustrated by solving a search in unsorted database in polynomial time by resonance between external force representing the address of a required item and the response representing the location of this item.

In the previous work in Ref.[1], we presented a new interaction scheme that describes the interaction of thermodynamic systems. Using this interaction scheme, we showed that the interactions of dark matter and dark energy are chaotic. We also predicted that the results could be generalized to all particle and thermodynamic systems. In addition, we gave physical definitions of the concepts of chaos and self-organization. More importantly, we proposed a new law of physics based on interacting systems. In this study, we will consider two thermodynamic systems interacting under different conditions to prove the universality of the physical law we propose. We will show that these systems also have chaotic interaction dynamics.

This short report contains a result that characterizes almost global pullback attractor of discrete-time non-autonomous systems. Analogously to the multiple Lyapunov functions approach for switched systems, we show here that existence of multiple Lyapunov densities implies pullback convergence of almost all initial states to the origin for a discrete-time non-autonomous system.

In this work, an analytical and numerical analysis of the transition to chaos in five nonlinear systems of ordinary and partial differential equations, which are models of the autocatalytic chemical processes and the numbers of interacting populations, is carried out. It is analytically and numerically shown that in all considered systems of equations, further complication of the dynamics of solutions and the transition to chemical and biological turbulence is carried out in full accordance with the universal Feigenbaum-Sharkovsky-Magnitskii bifurcation theory through subharmonic and homoclinic cascades of bifurcations of stable limit cycles. In this case, irregular (chaotic) attractors in all cases are exclusively singular attractors in the sense of the FShM theory.

The theory of the origin of carcinomas suggests that neoplasias from epithelial tissues are the consequence of the reactivation of developmental programs. It proposes a model in which the epithelial cells undergo cellular transitions due to replicative senescence and inflammation towards a mesenchymal-undifferentiated phenotype with cancerous behavior. The conserved pattern of histological progression and the molecular biology of carcinomas is congruent with the view of cancer as a developmental disease. In support of the theory, the experimental literature regarding the molecular, cellular, and histopathological mechanisms associated with epithelial carcinogenesis were aligned according to the premises of the hypothesis. Thereby identified a generic process in the carcinogenesis of the breast, endometrium, prostate, colon, lung, pancreas, bladder, liver, and cervix. Then, is provided a methodology overview of modeling in systems biology derived from previous research testing the hypothesis. The results illustrate the value of the complex systems approach to recover behavior that cannot be inferred only by traditional methods. Specifically, the model suggests that the consistency in the cell types and the directionality of the observed cellular transitions during epithelial carcinogenesis arise from structural constraints in the molecular networks associated with the carcinomas. Overall, the results of the dynamical analysis agree with the premises of the hypothesis and provide an insightful perspective of the potential mechanisms underlying the cellular plasticity displayed during epithelial carcinogenesis. In an era of big data and yet few advances in the underlying causes of chronic diseases, the manuscript also aims to inspire molecular biologists to integrate existing empirical evidence with systems biology modeling in the pursuit of understanding.

Being able to express broad families of equivariant or invariant attributed graph functions is a popular measuring stick of whether graph neural networks should be employed in practical applications. However, it is equally important to learn deep local minima of losses (i.e., with much smaller loss values than other minima), even when architectures cannot express global minima. In this work we introduce the architectural property of attracting GNN optimization trajectories to local minima as a means of achieving smaller losses. We take first steps in satisfying this property for losses defined over attributed undirected unweighted graphs with a novel architecture, called Universal Local Attractor (ULA). The latter refines each dimension of end-to-end trained node feature embeddings based on graph structure to track the optimization trajectories of losses satisfying some mild conditions. The refined dimensions are then linearly pooled to create predictions. We experiment on 10 tasks, from node classification to clique detection, on which ULA is comparable with or significantly outperforms popular alternatives of similar or greater theoretical expressive power.

A lightweight image encryption algorithm based on chaos induction via a 5-dimensional hyperjerk oscillator (5DHO) is presented. First, the dynamics of our 5DHO network is investigated and shown to exhibit up to five coexisting hidden attractors in the state space that depend exclusively on the system’s initial values. Further, a simple implementation of the circuit was used to validate its ability to exhibit chaotic dynamical properties. Second, an Arduino UNO platform is used to confirm the usability of our oscillator in digital implementation of the system. Finally, an efficient image encryption application is executed using the proposed chaotic networks based on the use of permutation-substitution sequences. The superior qualities of the proposed strategy are traced to the dynamic set of keys used in the substitution process which heralds the generation of the final ciphered image. Based on the results obtained from the entropy analysis (7.9976), NPCR values (99.62), UACI tests (33.69) and encryption execution time for 512x512 images (0.1179 sec), the proposed algorithm is adjudged to be fast and robust to differential and statistical attacks relative to similar approaches.

The work is devoted to the study of a MEMS resonator dynamics under the action of phase-locked and automatic gain control loops. Particular attention is directed to the study of the nonlinearity factor of the resonator elastic restoring force. It was found that the determination of control system parameters based on the stability analysis of the operating resonant mode, in the general case, does not provide the required phase adjustment and stabilization of the oscillation amplitude. Stable multifrequency modes of oscillations are found, an analytical study of the mechanisms of their appearance and evolution is carried out under variation of the key parameters of the system. The real regions of the control system stable operation are determined (which do not coincide, as was found, with the regions of stability of the operating resonant mode, due to the presence of hidden attractors in the phase space of the system). A methodology has been developed for identifying such areas of stable operation. A significant complication of the structure of possible motions in the system with an increase in the Q-factor of the resonator is revealed.

Waddington’s epigenetic landscape, a famous metaphor in developmental biology, depicts how a stem cell progresses from an undifferentiated phenotype to a differentiated one. The concept of “landscape” in the context of dynamical system theory represents a high-dimensional cell state space, in which each cell phenotype is considered as an “attractor” that is determined by interactions among multiple variables (molecular players), and is buffered against environmental fluctuations. Further, biological noise is thought to play an important role during these cell-fate decisions and in fact controls transitions between different phenotypes. Here, we discuss these phenotypic transitions in cancer from a dynamical systems perspective and invoke the concept of “cancer attractors” – hidden stable states of the underlying regulatory network that are not occupied by normal cells. Using epithelial-to-mesenchymal transition (EMT), cancer stem-like properties, metabolic reprogramming and the emergence of drug/hormone resistance as examples, we illustrate how phenotypic plasticity in cancer cells enables them to acquire hybrid phenotypes (such as hybrid epithelial/mesenchymal and hybrid metabolic phenotypes) that tend to be more aggressive and notoriously resilient to drug/hormone treatment. Furthermore, we highlight multiple factors that may give rise to phenotypic plasticity in cancer cells, such as (a) multi-stability or oscillatory behaviors governed by underlying regulatory networks involved in cell-fate decisions in cancer cells, and (b) network rewiring due to conformational dynamics of intrinsically disordered proteins (IDPs) that are highly enriched in cancer cells. We conclude by discussing why a therapeutic approach that promotes ‘recanalization’, i.e. the exit from “cancer attractors” and re-entry into “normal attractors”, is more likely to succeed rather than a conventional approach that targets individual molecules/pathways.