Shirin Panahi

• Ph.D.
• PostDoc at Arizona State University

For anticipating critical transitions in complex dynamical systems, the recent approach of parameter-driven reservoir computing requires explicit knowledge of the bifurcation parameter. We articulate a framework combining a variational autoencoder (VAE) and reservoir computing to address this challenge. In particular, the driving factor is detected...

A foundational machine-learning architecture is reinforcement learning, where an outstanding problem is achieving an optimal balance between exploration and exploitation. Specifically, exploration enables the agents to discover optimal policies in unknown domains of the environment for gaining potentially large future rewards, while exploitation re...

Anticipating a tipping point, a transition from one stable steady state to another, is a problem of broad relevance due to the ubiquity of the phenomenon in diverse fields. The steady-state nature of the dynamics about a tipping point makes its prediction significantly more challenging than predicting other types of critical transitions from oscill...

Exceptional points, a remarkable phenomenon in physical systems, have been exploited for sensing applications. It has been demonstrated recently that it can also utilize as sensory threshold in which the interplay between exceptional-point dynamics and noise can lead to enhanced performance. Most existing works focused on second-order exceptional p...

Deep learning models have revolutionized various domains, with Multi-Layer Perceptrons (MLPs) being a cornerstone for tasks like data regression and image classification. However, a recent study has introduced Kolmogorov-Arnold Networks (KANs) as promising alternatives to MLPs, leveraging activation functions placed on edges rather than nodes. This...

Data-driven model discovery of complex dynamical systems is typically done using sparse optimization, but it has a fundamental limitation: sparsity in that the underlying governing equations of the system contain only a small number of elementary mathematical terms. Examples where sparse optimization fails abound, such as the classic Ikeda or optic...

The Atlantic Meridional Overturning Circulation (AMOC) is a significant component of the global ocean system, which has so far ensured a relatively warm climate for the North Atlantic and mild conditions in regions, such as Western Europe. The AMOC is also critical for the global climate. The complexity of the dynamical system underlying the AMOC i...

Adaptive networks with time-varying connectivity, often called plasticity, provide a fundamental paradigm to model complex dynamical systems. In these systems, different groups of elements frequently exhibit different yet synchronized dynamics within each group. Here we propose a framework to study patterns of synchronous solutions in a large class...

This article presents an extremum‐seeking control (ESC) algorithm for unmodeled nonlinear systems with known steady‐state gain and generally non‐convex cost functions with bounded curvature. The main contribution of this article is a novel gradient estimator, which uses a polyhedral set that characterizes all gradient estimates consistent with the...

Reinforcement learning (RL) has been employed to devise the best course of actions in defending the critical infrastructures, such as power networks against cyberattacks. Nonetheless, even in the case of the smallest power grids, the action space of RL experiences exponential growth, rendering efficient exploration by the RL agent practically unatt...

A problem in nonlinear and complex dynamical systems with broad applications is forecasting the occurrence of a critical transition based solely on data without knowledge about the system equations. When such a transition leads to system collapse, as often is the case, all the available data are from the pre-critical regime where the system still f...

In an ecosystem, environmental changes as a result of natural and human processes can cause some key parameters of the system to change with time. Depending on how fast such a parameter changes, a tipping point can occur. Existing works on rate-induced tipping, or R-tipping, offered a theoretical way to study this phenomenon but from a local dynami...

Systems that synchronize in nature are intrinsically different from one another, with possibly large differences from system to system. While a vast part of the literature has investigated the emergence of network synchronization for the case of small parametric mismatches, we consider the general case that parameter mismatches may be large. We pre...

This perspective reviews the subject of synchronization in networks of coupled non-phase oscillators in the presence of parametric mismatches. We first discuss the case of small parametric mismatches, for which the conditions for stability of the synchronous solution are the same as in the case of identical oscillators, but the synchronization erro...

Systems that synchronize in nature are intrinsically different from one another, with possibly large differences from system to system. While a vast part of the literature has investigated the emergence of network synchronization for the case of small parametric mismatches, we consider the general case that parameter mismatches may be large. We pre...

In this paper, we study the network pinning control problem in the presence of two different types of coupling: (i) node-to-node coupling among the network nodes and (ii) input-to-node coupling from the source node to the “pinned nodes.” Previous work has mainly focused on the case that (i) and (ii) are of the same type. We decouple the stability a...

In this paper, we study the network pinning control problem in the presence of two different types of coupling: (i) node-to-node coupling among the network nodes and (ii) input-to-node coupling from the source node to the `pinned nodes'. Previous work has mainly focused on the case that (i) and (ii) are of the same type. We decouple the stability a...

The study of the synchronization phenomenon in the functional brain networks of individuals with Attention Deficit Hyperactivity Disorder (ADHD) has always been of interest to researchers. ADHD is a prevalent psychiatric disorder among children, which in addition to other problems, makes it difficult to recognize facial emotions correctly. However,...

The main motivation for this paper is to characterize network synchronizability for the case of cluster synchronization (CS), in an analogous fashion to Barahona and Pecora [Phys. Rev. Lett. 89, 054101 (2002)] for the case of complete synchronization. We find this problem to be substantially more complex than the original one. We distinguish betwee...

Attention Deficit Hyperactivity Disorder (ADHD) is a common neurodevelopmental disorder that, in addition to inattention, excessive activity, or impulsivity, makes it difficult for children to process facial emotions and thus to interact with their peers. Here we analyze neuronal networks of children with this disorder by means of the phase-locking...

Instinct delay in biological systems is a significant parameter in analyzing complex biological systems like neuronal networks. Also, considering the interactive neurons in complex networks, a new window is opened into computational neuroscience. This paper aims to analyze the time delays in a multi-layer lattice with asymmetric bidirectional coupl...

We respond briefly to a comment [1, arXiv:2110.15493] recently posted online on our paper [2, arXiv:2108.07893]. Complete and cluster synchronization of random networks is undoubtedly a topic of interest in the Physics, Engineering, and Nonlinear Dynamics literature. In [3] we study both complete and cluster synchronization of networks and introduc...

We discuss here the application of the simultaneous block diagonalization (SBD) of matrices to the study of the stability of both complete and cluster synchronization in random (generic) networks. For both problems, we define indices that measure success (or failure) of application of the SBD technique in decoupling the stability problem into probl...

Autapse is introduced as a self-feedback connection that connects the dendrites and axons of the same neuron. Previous studies have revealed that the existence of the autapse can influence the synchronized behaviours of the coupled neurons. In this paper, the chimera state is studied in the presence of autaptic connections. To this aim, a regular n...

Group synchronization arises when two or more synchronization patterns coexist in a network formed of oscillators of different types, with the systems in each group synchronizing on the same time evolution, but systems in different groups synchronizing on distinct time evolutions. Group synchronization has been observed and characterized when the s...

The main motivation for this paper is to present a definition of network synchronizability for the case of cluster synchronization, similar to the definition introduced by Barahona and Pecora for the case of complete synchronization. We find this problem to be substantially more complex than the original one. We distinguish between the cases that t...

We study cluster synchronization of networks and propose a canonical transformation for simultaneous block diagonalization of matrices that we use to analyze the stability of the cluster synchronous solution. Our approach has several advantages as it allows us to: (1) decouple the stability problem into subproblems of minimal dimensionality while p...

Group synchronization arises when two or more synchronization patterns coexist in a network formed of oscillators of different types, with the systems in each group synchronizing on the same time-evolution, but systems in different groups synchronizing on distinct time-evolutions. Group synchronization has been observed and characterized when the s...

We study cluster synchronization of networks and propose a canonical transformation for simultaneous block diagonalization of matrices that we use to analyze stability of the cluster synchronous solution. Our approach has several advantages as it allows us to: (1) decouple the stability problem into subproblems of minimal dimensionality while prese...

We discuss here the application of the simultaneous block diagonalization (SBD) of matrices to the study of the stability of both complete and cluster synchronization in random (generic) networks. For both problems, we define indices that measure success (or failure) of application of the SBD technique in decoupling the stability problem into probl...

One-dimensional (1D) map-based neuron models are of significant interest according to their simplicity of simulation and ability to mimic real neurons’ complex behaviors. A fractional-order 1D neuron map is proposed in this paper. Dynamical characteristics of the model are analyzed by obtaining bifurcation diagrams and the Lyapunov exponents’ diagr...

A new 4D memristive chaotic system with an infinite number of equilibria is proposed via exhaustive computer search. Interestingly, such a new memristive system has a plane of equilibria and two other lines of equilibria. Lyapunov exponent and bifurcation analysis show that this system has chaotic solutions with coexisting attractors. The basins of...

We study the synchronization of coupled identical circulant and non-circulant oscillators using single variable and different multi-variable coupling schemes. We use the master stability function to determine conditions for synchronization, in particular the necessary coupling parameter that ensures a stable synchronization manifold. We show that f...

Complex networks are of major importance in many areas of science. The network property analysis of such networks can help researchers to understand many real-world systems. Different collective phenomena emerge in complex networks, synchronization is one of the most interesting states. The number of links plays a major role in synchronizability. I...

Chaotic jerk oscillators belong to the simplest chaotic systems. These systems try to model the behavior of dynamical systems efficiently. Jerk oscillators can be known as the most general systems in science, especially physics. It has been proved that every dynamical system expressed with an ordinary differential equation is able to describe as a...

The category of the small-world networks is neither random (like random networks) nor highly ordered (like regular networks). Their special properties are the combination of high clustering coefficient and short path length which can be seen in many real world networks. Synchronization of a small-world topology of dynamical network receives a great...

Models of neurons play an essential role in computational neuroscience. They provide a virtual laboratory to analyze the different regimes in the electrical activities of a single neuron or a network of neurons. They help the neuroscientist to have a better look at the nervous system. Some researchers have claimed that the transition of the ions th...

Synchronization in complex networks is an evergreen subject with numerous applications in biological, social, and technological systems. We here study whether a transition from a single variable to multivariable coupling facilitates the emergence of synchronization in a network of circulant oscillators. We show that the network indeed has much bett...

The heart is the essential, yet complex, component of the human cardiovascular system. In the past few decades, researchers have taken giant steps toward better understanding of the cardiac system and there have been proposed some mathematical models to describe the heart's function. In this paper, a new Fitzhugh-Nagumo neuron (FNN) model is propos...

Computational models play an essential role in studying and predicting the behavior of a bio-system. Discrete dynamical models, usually known as maps, are important, especially when it comes to the mathematical study of the behavior of the neurons and neural network. Map-based neural models are simple, yet powerful and computationally efficient too...

Investigating the stability of the synchronization manifold is a critical topic in the field of complex dynamical networks. Master stability function (MSF) is known as a powerful and efficient tool for the study of synchronization in complex identical networks. The network can be synchronized whenever the MSF is negative. MSF uses the Lyapunov or F...

In this paper, a new four-dimensional nonlinear oscillator is introduced. This oscillator is memristive and can exhibit chaotic behavior. A complete dynamical analysis is done on each parameter of this system by the help of bifurcation diagram and Lyapunov exponents’ diagram. In order to estimate parameters of the proposed system, we use a new cost...

Investigating biological systems from the viewpoint of complex systems has attracted noticeable attention during the last decades. In this paper biochemical cell cycle is investigated. Cell cycle process is controlled by the complex network of different interacting proteins. However, the study of a cell cycle in a network has been less considered....

There is a growing attraction to memristive chaotic systems since last decades. This paper provides a complete dynamical analysis of a chaotic memristive jerk system. Complex behavior of this system is studied with the help of equilibrium analysis, state space plots of trajectories, and bifurcation and Lyapunov exponents’ diagrams. The equilibrium...

Chimera states have been a vibrant subject of research in the recent past, but the analytical treatment of transitions from chimeras to coherent states remains a challenge. Here we analytically derive the necessary conditions for this transition by means of the coherent stability function approach, which is akin to the master stability function app...

Chimera states have been a vibrant subject of research in the recent past, but the analytical treatment of transitions from chimeras to coherent states remains a challenge. Here we analytically derive the necessary conditions for this transition by means of the coherent stability function approach, which is akin to the master stability function app...

Epilepsy is a prevalent neurological disorder with symptoms characterized by abnormal discharge in the brain. According to the classification of the International League Against Epilepsy (ILAE) Commission, temporal lobe epilepsy is the most common type of epilepsy accounting for the most cases of the disorder observed in patients. Electroencephalog...

These days, investigating different aspects of new chaotic systems with hidden attractors is one of the most interesting topics in chaos theory. In this chapter, a new 4D hyperjerk chaotic system is presented. The proposed system has no equilibria, so it belongs to the class of systems with hidden attractors. Dynamical features of this system such...

In this chapter, focus will be on parameter estimation methods of chaotic systems. A so called density estimation approach will be considered and its application in a chaotic system identification problem will be described. The estimation method is based on the attractor distribution modeling in the state space using a Gaussian mixture model (GMM)....

In this article a simple chaotic flow with hidden attractor is proposed. Various dynamics of this new system such as periodic and chaotic oscillations can be achieved by setting bifurcation parameters in a proper value. Nowadays chaos based engineering applications like encryption and hiding data face some significant problems. Chaotic systems with...

Designing new chaotic system with specific features is an interesting field in nonlinear dynamics. In this paper, some new chaotic systems with cyclic symmetry are proposed. In order to understand the overall behavior of such systems, the dynamical analyses such as stability analysis, bifurcation and Lyapunov exponent analysis are done. The accurat...

Two simple chaotic maps without equilibria are proposed in this paper. All nonlinearities are quadratic and the functions of the right-hand side of the equations are continuous. The procedure of their design is explained and their dynamical properties such as return map, bifurcation diagram, Lyapunov exponents, and basin of attraction are investiga...

In the last decades, many studies have been done about nervous system from the mathematical and computational point of view. Many mathematical models have been proposed to describe neuron. Most of them have described the membrane potential of a neuron in terms of the leakage current and the synaptic inputs. Very recently, according to the Maxwell e...

Nowadays, designing chaotic systems with hidden attractor is one of the most interesting topics in nonlinear dynamics and chaos. In this paper a new 4D chaotic system is proposed. This new chaotic system has no equilibria, so it belongs to the category of systems with hidden attractors. Dynamical features of this system are investigated by the help...

In this paper, we discuss how chaotic systems show the importance of imperfection. This happens through the butterfly effect. Then we discuss that chaotic systems with extreme multi-stability can much better demonstrate such importance. The reason is that in such systems not only the quantity of time-series is affected by butterfly effect, but also...

Discovering unknown aspects of no-equilibrium systems with hidden strange attractors is an attractive research topic. A novel quadratic hyperjerk system is introduced in this paper. It is noteworthy that this no-equilibrium system can generate hidden chaotic attractors. The essential properties of such systems are investigated by means of equilibri...

In this paper, we introduce a new chaotic system that is used for an engineering application of the signal encryption. It has some interesting features, and its successful implementation and manufacturing were performed via a real circuit as a random number generator. In addition, we provide a parameter estimation method to extract chaotic model pa...

Epilepsy is a long-term chronic neurological disorder that is characterized by seizures. One type of epilepsy is simple partial seizures that are localized to one area on one side of the brain, especially in the temporal lobe, but some may spread from there. GABA (gamma-aminobutyric acid) is an inhibitory neurotransmitter that is widely distributed...

For non-invasively investigating the interaction between insulin and glucose, mathematical modeling is very helpful. In this paper, we propose a new model for insulin-glucose regulatory system based on the well-known prey and predator models. The results of previous researches demonstrate that chaos is a common feature in complex biological systems...

Computational modeling plays an important role in prediction and optimization of real systems and processes. Models usually have some parameters which should be set up to the proper value. Therefore, parameter estimation is known as an important part of the modeling and system identification. It usually refers to the process of using sampled data t...

In this article, a simple autonomous transiently chaotic flow with cubic nonlinearities is proposed. This system represents some unusual features such as having a surface of equilibria. We shall describe some dynamical properties and behaviours of this system in terms of eigenvalue structures, bifurcation diagrams, time series, and phase portraits....

Parameter estimation plays an important role in modeling and system identification. However, parameter estimation of chaotic systems has some basic differences with other dynamical systems due to butterfly effect. In this paper, we apply a new cost function for parameter estimation in a very interesting chaotic system, a system with a plane of equi...