Jay Prakash Singh

• PhD
• Professor (Assistant) at Visvesvaraya National Institute of Technology

This paper presents a novel memristor-based magnetized Hopfield neural network (HNN) designed for generating and controlling hidden scroll chaotic attractors with reduced input complexity. The integration of memristor introduces nonlinear dynamics, enhancing the network’s ability to produce complex chaotic behaviour. By magnetizing the Hopfield mod...

Many papers are reported in the literature on applying chaotic/hyperchaotic systems for secured communication. Very few papers have discussed the robustness and effectiveness of their communication strategy. In this paper, first, an integral sliding surface-based fast-terminal sliding mode control is designed to synchronise two identical, highly co...

To provide a sustainable energy infrastructure, the need for renewable energy development is necessary and we need to develop a multi-port bidirectional DC-DC converter topologies to control the power flow among the modules such as photo voltaic (PV), batteries, energy storage systems (ESS), load, and grid. This paper discusses the various bidirect...

Synchronisation of chaotic systems has been finding its real-life applications and has drawn the attention of researchers. In this paper, the complete synchronisation between two identical identical memristors chaotic systems in the presence of parameter uncertainty and disturbances are considered. An available, conventional adaptive controller is...

The synchronisation between two identical chaotic\hyperchaotic systems has been an interesting research problem in the last two decades. Many works have been reported on the synchronisation of chaotic\hyperchaotic systems using adaptive controllers. In most of these papers, the number of control inputs equals the number of the system states, and th...

The paper reports a modified 4D autonomous hyperchaotic system with an unusual characteristic. The modified system exhibits dissipative behavior for some ranges of a parameter and conservative behavior for the other ranges of the same parameter. Thus, there is a switching between dissipative and conservative behaviors of the proposed system. In the...

Chaotic systems with cyclic symmetry are very rare and have been less discussed in the literature. Similarly, megastable oscillators, which can have a finite or infinite number of coexisting attractors, have also attracted researchers. We propose a class of cyclic symmetry oscillators with the megastable property with infinite coexisting attractors...

In the last two years, many chaotic or hyperchaotic systems with megastability have been reported in the literature. The reported systems with megastability are mostly developed from their dynamic equations without any reference to the physical systems. In this paper, the dynamics of a single-link manipulator is considered to observe the existence...

This paper reports a modified 2D periodically forced oscillator. Numerical simulation results using the phase portrait and Lyapunov exponents’ spectrum say that the proposed oscillator depicts megastability. Offset boosting in the new system is shown using the variable boostable phenomenon. Very limited research is available on such type of oscilla...

In the past few years, chaotic systems with megastability have gained more attention in research. However, megastability behavior is mostly seen in chaotic systems. In this paper, a new 4D autonomous hyperjerk hyperchaotic system with megastability is reported.The new system has two modes of operation. The first mode considers one of its parameters...

This paper presents a novel simple 4-D dissipative autonomous hyperchaotic system with a saddle-point index-2 equilibrium point. The dynamics of the new system consists of nine terms with two nonlinear terms. Thus, the proposed system is one of the simplest 4-D hyperchaotic systems. The new system also shows multistability behavior for some range o...

A projective synchronisation strategy is designed in this paper to synchronise a master manipulator having 12 states modelled using the assumed modes method and the slave manipulator with 8 states modelled using the lumped parameter method. The first objective is to design an adaptive SMC-based filter and the second objective is to design an adapti...

In this paper, the chaotic phenomenon is reported in a bearing system. The chaotic dynamics of the new system is first derived from an available bearing system. The proposed system is then analyzed using various tools to observe its dynamical behaviors. Theoretical and simulation results confirm the presence of chaotic and periodic behaviors in the...

In this paper, we have proposed a new chaotic megastable oscillator which has both conservative and dissipative characters depending on the selection of parameters. Various dynamical characteristics including megastability of the new system are investigated and presented. The bifurcation plots and the corresponding Lyapunov exponents confirm the ex...

In the literature of dynamical systems, many papers are seen on the synchronisation between chaotic/hyperchaotic systems. In these reported works, the synchronisation is done when the external disturbances are added to state of the slave system where controller is added, i.e. using matched disturbances. Occasional work is reported on the synchronis...

Objectives of the paper are to (i) develop a new hyperchaotic system having hidden attractors and (ii) to show the applications using the new system in the form of secure communication. New system proposed in the paper has a stable equilibrium, hence considered under the class of the hidden attractors dynamical system. Dynamical characteristics of...

In this paper, a new chaotic oscillator consists of a single op-amp, two capacitors, one resistor, one inductor, and memristive diode bridge cascaded with an inductor is proposed. The proposed chaotic oscillator has a line of equilibria. In the new oscillator circuit, negative feedback, i.e. inverting terminal of the op-amp is used, and the non-inv...

The objective of this Letter is to report the development of the simplest hyperchaotic system in comparison with all existing simplest hyperchaotic systems. The proposed system does not contain any non-linear (product, quadratic or cubic) term and has a total of eight terms including the only one piecewise linear term. The circuit of the proposed s...

This paper attempts to find some interesting and unique properties in the dynamics of a permanent magnet synchronous motor (PMSM). When compared with the existing literature on the dynamics of a PMSM, we find some interesting and unique behaviors which have not been reported so far. These are (i) occurrence of multistability, (ii) existence of hidd...

In this paper, we discuss a new fractional-order memristor-based three-dimensional chaotic system with a stable equilibrium point. The proposed system belongs to the category of hidden attractors dynamical system. The system is new in the sense that it is a fractional-order memristor-based chaotic system and exhibits hidden attractors. The chaotic...

Very little research is available on megastability in chaotic systems. In this paper, megastability in a new chaotic system with dissipative and conservative nature is reported. The new system is a quasi-periodically forced damped double well excitation system. Three different cases are considered for our study. In one case, the new system has diss...

In recent years, flexible manipulators (FMs) have become more attractive and are being used in many fields due to their advantages such as their light weight, low energy consumption, smaller size, etc. The desired trajectory tracking or path planning problem for a flexible robot manipulator is interesting and challenging. Path planning for a FM req...

This paper reports a new simple 4-D hyperjerk chaotic system. The proposed system has only one stable equilibrium point. Hence, its strange attractor belongs to the category of hidden attractors. The proposed system exhibits various dynamical behaviours including chaotic, periodic, stable nature and coexistence of various attractors. Numerous theor...

In this paper, a synchronisation strategy between a controlled master and three-slave two-link flexible manipulators is proposed. Two out of the three slaves are identical with the master, whereas the third one is non-identical. The master and the slave manipulators are modelled by assumed modes and lumped parameter methods, respectively. The 12 st...

Hidden attractors with the family of stable equilibrium points in higher-dimensional systems are more interesting and difficult discover compared to other families of hidden attractors. In this paper, a new 5D hyperchaotic system is reported. The proposed system has only one stable equilibrium point. Hence, the new system belongs to the category of...

This paper attempts to construct a new 3-D chaotic system which is easily hardware realisable and fulfil the requirement of a real-life application. The proposed system is relatively more chaotic (based on the first Lyapunov exponent) and has larger bandwidth than 50 available chaotic systems. Lyapunov spectrum and bifurcation diagram of the system...

A sinusoidally-driven conservative and dissipative system with signum nonlinearity is presented in this paper. The proposed system exhibits strange attractors, multistability, and megastability. The system exhibits both conservative and dissipative behaviors with the change of its parameters. The Lyapunov exponents, Lyapunov spectrum plots, bifurca...

Very little research is available in the field of 4-D autonomous conservative chaotic systems. This paper presents five new 4-D autonomous conservative chaotic systems having non-hyperbolic equilibria with various characteristics. The proposed systems have different numbers of non-hyperbolic equilibrium points. One of the new systems has four non-h...

In recent years, chaotic systems with no equilibrium point are the hottest topic for research as these systems can have neither homoclinic nor heteroclinic orbits and show hidden attractors. This paper presents a novel fractional-order memristor-based chaotic jerk system with no equilibrium point. The proposed system is new in the sense that it is...

The finding of hidden attractors in a chaotic/hyperchaotic system is more important, interesting and difficult than a self-excited attractor. This paper reports a new simple 4-D chaotic system with no equilibrium point and having hidden attractors with the coexistence of attractors (i.e. multistability). The proposed system has a total of eight ter...

In this paper, we present a new quasi-periodically forced system which exhibits coexistence of an infinite number of nested attractors (megastability) along with quasi-periodic and multistable behaviours. The dynamical behaviour of the system is analysed using the Lyapunov exponents, Lyapunov spectrum, bifurcation diagrams, and phase plots. An anal...

Objectives of the paper are (1) to design two new real and complex no equilibrium point hyperchaotic systems, (2) to design synchronisation technique for the new systems using the contraction theory and (3) to validate the results by using circuit realisation. First a new no equilibrium point hyperchaotic system is developed using a 3-D generalised...

This paper presents a new four-dimensional (4D) autonomous chaotic system which has first Lyapunov exponent of about 22 and is comparatively larger than many existing three-dimensional (3D) and 4D chaotic systems. The proposed system exhibits hyperbolic curve and circular paraboloid types of equilibria. The system has all zero eigenvalues for a par...

In the present decade, chaotic systems are used and appeared in many fields like in information security, communication systems, economics, bioengineering, mathematics, etc. Thus, developing of chaotic dynamical systems is most interesting and desirable in comparison with dynamical systems with regular behaviour. The chaotic systems are categorised...

Robotics is an emerging and interesting area in many fields of technical science. In general, a robot manipulator (rigid/flexible) is a more focused research direction in comparison with other areas of robotics. Specifically, flexible manipulators are more applicable in many fields when compared with its rigid counterparts because of many advantage...

This paper reports 4-D hyperchaotic and chaotic systems with various quadric surfaces of equilibria. A known and systematic search procedure is used to generate the proposed systems. Six cases have non-degenerate quadric surfaces (ellipsoid, spheroid, sphere, elliptic hyperboloid of one sheet, circular hyperboloid of one sheet) type of equilibria a...

The objectives of the paper are (i) to develop a new 4-D conservative chaotic system and (ii) to design an LMI based integral SMC for tracking control of the proposed system. The proposed system has hidden chaotic orbits with no equilibrium point and transient chaotic behaviour. The proposed controller is designed for controlling the transient chao...

This paper reports various chaotic phenomena that occur in a single-link flexible joint (SLFJ) robot manipulator. Four different cases along with subcases are considered here to show different types of chaotic behaviour in a flexible manipulator dynamics. In the first three cases, a partial state feedback as joint velocity and motor rotor velocity...

The objectives of the paper are (i) to develop a new 4-D conservative chaotic system with hidden chaotic orbits, (ii) to design a second order adaptive time varying sliding mode control for the synchronization between two identical proposed chaotic systems in the presence of matched disturbances and (iii) to compare the performances of the proposed...

The paper reports the simplest 4-D dissipative autonomous chaotic system with line of equilibria and many unique properties. The dynamics of the new system contains a total of eight terms with one nonlinear term. It has one bifurcation parameter. Therefore, the proposed chaotic system is the simplest compared with the other similar 4-D systems. The...

This paper reports a new 4-D dissipative chaotic system. When compared with the available 4-D chaotic/hyperchaotic systems, the unique properties of the proposed system are (i) the system exhibits coexistence of different kind of asymmetric hidden attractors, (ii) the system has a curve of equilibria and (ii) the system is simple. This system does...

The objectives of this paper are synchronisation and anti-synchronisation between a hyperchaotic and a chaotic systems using nonlinear active control (NAC) scheme, its analogue circuit design and application to secure communication. Hyperchaotic Lorenz–Stenflo system is used as a master and the chaotic (a hyperchaotic system in its chaotic state) C...

This paper presents a control technique for a many equilibria hyperchaotic system. Controlling a many equilibria hyperchaotic system is a challenging task. An adaptive proportional integral SMC is proposed for controlling of a hyperchaotic system. In the proposed control technique, the sliding surfaces are designed with unknown constant gains. Alth...

In this paper, synchronization and anti-synchronization of Bhalekar-Gejji chaotic system is proposed with application to secure communication. Further its analog circuit design and simulation is carried out using analog components. Proposed synchronization and anti-synchronization with application to secure communication is achieved using robust SM...

In this paper, new results are devised based on sliding mode control (SMC) using Proportional- Integral switching surface and Active control schemes for synchronization of two different chaotic systems Chen and Liu-Yang chaotic system. Lyapunov stability theory is used to achieve stability of designed switching surface for proposed synchronization...

This paper puts forward the construction of a new chaotic system based on anti-control of chaos. The Bhalekar-Gejji (BG) chaotic system undergoes chaotification in order to generate chaos. Chaotification is achieved by destabilising the equilibria. The novelty of the paper is that the BG system is subjected to chaotification for the very first time...

The objective of the paper is to develop a novel hyperchaotic system with a line of equilibria and sigma shaped Poincare map. The proposed hyperchaotic system has unstable and stable equilibria based on the values of the state variable. The system is relatively simpler than the reported hyperchaotic systems with a line of equilibria. The proposed s...

This paper reports a new 3-D autonomous chaotic system with novel behaviour. The proposed system has three different natures of equilibria: (i) saddle, (ii) saddle foci and (iii) stable node foci which is new in the literature. The system has invariant nature of the equilibria in the considered ranges of all five bifurcation parameters. The system...

This review paper aims at answering a basic question on the sign of Lyapunov exponents. A few recent papers reported hyperchaotic system having the sign of Lyapunov exponents as (+, +, −, −). Such (+, +, −, −) sign of Lyapunov exponents is in contradiction with the well known (+, +, 0, −) sign of Lyapunov exponents for a 4-D hyperchaotic system. Th...

Some comments on the paper ?Theoretical Analysis and Circuit Verification for Fractional-Order Chaotic Behavior in a New Hyperchaotic System? (L. Liu and C. Liu, 2014) are pointed out in this letter. It is shown in this letter that the claimed hyperchaotic system exhibits a periodic behaviour for the chosen parameters and initial condition. However...

In this paper a new 4-D conservative chaotic system is reported. When compared with other existing chaotic systems the proposed system has the following unique properties (i) hidden chaotic orbits with no equilibria and (ii) coexistence of chaotic orbits. The chaotic behaviour of the proposed conservative chaotic system is verified by finding the L...

The Objective of the paper is to develop a new asymmetric hyperchaotic system with more complexity. The system has two dissimilar equilibrium points. Non-uniform contraction and expansion of volume in phase space is also an important property of the proposed system. A hyperchaotic system with above characteristics is first time reported here. Detai...

The obective of the paper is to develop a new hyperchaotic system with a single equilibrium point. The system is more hyperchaotic, larger bandwidth and complex than many other reported hyperchaotic systems. The proposed hyperchaotic system has non-uniform contraction and expansion of volume in phase space. Different theoretical and numerical techn...

In this paper, master-slave synchronization scheme of non-identical hyperchaotic systems is discussed using the sliding mode control strategy. Hyperchaotic Lu system is considered as master and hyperchaotic Bao system as slave system. Lyapunov stability theory is used for stabilization and convergence of error dynamics. A proportional-integral (PI)...

In this paper Proportional-Integral (PI) switching surface based sliding mode control (SMC) for hybrid synchronization of two different chaotic systems is proposed and their circuit simulations are also shown. The chaotic Chen system is used as master system and chaotic Liu-Yang system is used as slave system. Lyapunov stability theory is used to a...

In this paper observer based synchronization of Lorenz-Stenflo (LS) chaotic system is proposed. Lyapunov stability theory is used to ensure the stability. The required Lyapunov stability condition which results in terms of nonlinear matrix inequality. To develop observer, these inequalities are further reformulated into Linear Matrix Inequality (LM...

In this paper, a scheme of global anti-synchronization between two identical newly developed Bhalekar–Gejji chaotic system is proposed. This anti-synchronization scheme is achieved by using nonlinear active control since the parameters of both the systems are known and states are measurable. Lyapunov stability theory is used to ensure stability of...

This paper aims towards synchronization of Bhalekar-Gejji chaotic system and its application to secure communication. Synchronization is achieved using suitable nonlinear active control (NAC) scheme. Proposed synchronization is used to achieve secure communication using NAC. For secure communication, the information signal is masked with one of the...

Hybrid synchronization based on the active control theory between two different chaotic systems, ie Lu and Bhalekar-Gejji is reported in this paper. Lu chaotic system is taken as master and Bhalekar-Gejji chaotic system as slave. Stabilization of error dynamics is achieved by satisfying the Lyapunov stability conditions. Control is designed by u...

This paper addresses the anti-synchronization problem of two Bhalekar-Gejji Chaoticsystems in the presence of unknown system parameters. Based on Lyapunov stabilitytheory an adaptive control law is devised to make the states of two identical Bhalekar-Gejji chaotic systems with unknown system parameters asymptotically synchronized.Finally, numerical...

This paper investigates hybrid synchronization between two non-identical hyperchaotic systems using sliding mode control (SMC) strategy. Hyperchaotic Lu system is considered as master and hyperchaotic Bao system as slave system. The stability results are established using PI (Proportional Integral) switching surface and Lyapunov stability theory fo...

In this paper, design of SMC scheme based controller is proposed for synchronization of two different hyperchaotic systems. Synchronization is achieved using the Lyapunov stability theory. A proportional integral (PI) switching surface is used to ensure the stability of the closed-loop error dynamics in sliding motion. This SMC scheme is effective...

In this paper hybrid synchronization between hyperchaotic and chaotic systems is presented. The hyperchaotic Lorenz-Stenflo system is used as master and the chaotic Chen system is used as slave. The global hybrid synchronization between master and slave systems is achieved by using nonlinear active control. Nonlinear controller is designed by using...

This paper addresses the anti-synchronization problem of two Bhalekar-Gejji Chaotic systems in the presence of unknown system parameters. Based on Lyapunov stability theory an adaptive control law is devised to make the states of two identical BhalekarGejji chaotic systems with unknown system parameters asymptotically synchronized. Finally, numeric...

In this paper synchronization of two different chaotic systems is proposed using Sliding Mode Control scheme. Lu chaotic system is used as master system and Bhalekar-Gejji chaotic system is used as slave system. Convergence of the synchronizing error is achieved using the Lyapunov stability theory. Synchronization of master and slave system is achi...